Elementary theories and hereditary undecidability for semilattices of numberings View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-05

AUTHORS

Nikolay Bazhenov, Manat Mustafa, Mars Yamaleev

ABSTRACT

A major theme in the study of degree structures of all types has been the question of the decidability or undecidability of their first order theories. This is a natural and fundamental question that is an important goal in the analysis of these structures. In this paper, we study decidability for theories of upper semilattices that arise from the theory of numberings. We use the following approach: given a level of complexity, say Σα0, we consider the upper semilattice RΣα0 of all Σα0-computable numberings of all Σα0-computable families of subsets of N. We prove that the theory of the semilattice of all computable numberings is computably isomorphic to first order arithmetic. We show that the theory of the semilattice of all numberings is computably isomorphic to second order arithmetic. We also obtain a lower bound for the 1-degree of the theory of the semilattice of all Σα0-computable numberings, where α≥2 is a computable successor ordinal. Furthermore, it is shown that for any of the theories T mentioned above, the Π5-fragment of T is hereditarily undecidable. Similar results are obtained for the structure of all computably enumerable equivalence relations on N, equipped with composition. More... »

PAGES

485-500

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00153-018-0647-y

DOI

http://dx.doi.org/10.1007/s00153-018-0647-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1107260582


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Novosibirsk State University", 
          "id": "https://www.grid.ac/institutes/grid.4605.7", 
          "name": [
            "Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090, Novosibirsk, Russia", 
            "Novosibirsk State University, 2 Pirogova St., 630090, Novosibirsk, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Bazhenov", 
        "givenName": "Nikolay", 
        "id": "sg:person.011333325747.16", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011333325747.16"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Nazarbayev University", 
          "id": "https://www.grid.ac/institutes/grid.428191.7", 
          "name": [
            "Department of Mathematics, School of Science and Technology, Nazarbayev University, 53, Qabanbaybatyr Avenue, 010000, Astana, Kazakhstan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Mustafa", 
        "givenName": "Manat", 
        "id": "sg:person.07664647506.18", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07664647506.18"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Kazan Federal University", 
          "id": "https://www.grid.ac/institutes/grid.77268.3c", 
          "name": [
            "Kazan Federal University, 18 Kremlevskaya Str., 420008, Kazan, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Yamaleev", 
        "givenName": "Mars", 
        "id": "sg:person.012726266747.26", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012726266747.26"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1002/malq.19550010205", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002259044"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1010521410739", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007013493", 
          "https://doi.org/10.1023/a:1010521410739"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10469-005-0016-x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023339347", 
          "https://doi.org/10.1007/s10469-005-0016-x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00739571", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025496460", 
          "https://doi.org/10.1007/bf00739571"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00739571", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025496460", 
          "https://doi.org/10.1007/bf00739571"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025812806", 
          "https://doi.org/10.1007/978-1-4615-0755-0_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025812806", 
          "https://doi.org/10.1007/978-1-4615-0755-0_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/jsl.2013.8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029607701"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0049-237x(99)80030-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030028047"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031120463", 
          "https://doi.org/10.1007/978-1-4615-0755-0_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031120463", 
          "https://doi.org/10.1007/978-1-4615-0755-0_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02218586", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032702944", 
          "https://doi.org/10.1007/bf02218586"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02218586", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032702944", 
          "https://doi.org/10.1007/bf02218586"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040782755", 
          "https://doi.org/10.1007/978-1-4615-0755-0_3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4615-0755-0_3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040782755", 
          "https://doi.org/10.1007/978-1-4615-0755-0_3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-68546-5_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044684096", 
          "https://doi.org/10.1007/978-0-387-68546-5_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-68546-5_2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1044684096", 
          "https://doi.org/10.1007/978-0-387-68546-5_2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02671553", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045623965", 
          "https://doi.org/10.1007/bf02671553"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02671553", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1045623965", 
          "https://doi.org/10.1007/bf02671553"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02219847", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046038075", 
          "https://doi.org/10.1007/bf02219847"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0049-237x(08)71260-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047970994"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/malq.19940400407", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051830997"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01190967", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052370847", 
          "https://doi.org/10.1007/bf01190967"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01190967", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052370847", 
          "https://doi.org/10.1007/bf01190967"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1023/a:1012516217265", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052873081", 
          "https://doi.org/10.1023/a:1012516217265"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/rm1965v020n04abeh001188", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058193782"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/logcom/exu066", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059876649"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2140/pjm.1986.122.319", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069069055"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-319-50062-1_25", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1087289194", 
          "https://doi.org/10.1007/978-3-319-50062-1_25"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/conm/257/04025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1089204430"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-05", 
    "datePublishedReg": "2019-05-01", 
    "description": "A major theme in the study of degree structures of all types has been the question of the decidability or undecidability of their first order theories. This is a natural and fundamental question that is an important goal in the analysis of these structures. In this paper, we study decidability for theories of upper semilattices that arise from the theory of numberings. We use the following approach: given a level of complexity, say \u03a3\u03b10, we consider the upper semilattice R\u03a3\u03b10 of all \u03a3\u03b10-computable numberings of all \u03a3\u03b10-computable families of subsets of N. We prove that the theory of the semilattice of all computable numberings is computably isomorphic to first order arithmetic. We show that the theory of the semilattice of all numberings is computably isomorphic to second order arithmetic. We also obtain a lower bound for the 1-degree of the theory of the semilattice of all \u03a3\u03b10-computable numberings, where \u03b1\u22652 is a computable successor ordinal. Furthermore, it is shown that for any of the theories T mentioned above, the \u03a05-fragment of T is hereditarily undecidable. Similar results are obtained for the structure of all computably enumerable equivalence relations on N, equipped with composition.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00153-018-0647-y", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.6741084", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1136186", 
        "issn": [
          "0933-5846", 
          "1432-0665"
        ], 
        "name": "Archive for Mathematical Logic", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3-4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "58"
      }
    ], 
    "name": "Elementary theories and hereditary undecidability for semilattices of numberings", 
    "pagination": "485-500", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "f106e8cbb053510248d64e1f30a2f2bf9564c1b257bf29002dcbf05557acf36c"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00153-018-0647-y"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1107260582"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00153-018-0647-y", 
      "https://app.dimensions.ai/details/publication/pub.1107260582"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:05", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000366_0000000366/records_112064_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs00153-018-0647-y"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00153-018-0647-y'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00153-018-0647-y'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00153-018-0647-y'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00153-018-0647-y'


 

This table displays all metadata directly associated to this object as RDF triples.

163 TRIPLES      21 PREDICATES      49 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00153-018-0647-y schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N5082e2b37ea4484f98843753344f9ffb
4 schema:citation sg:pub.10.1007/978-0-387-68546-5_2
5 sg:pub.10.1007/978-1-4615-0755-0_2
6 sg:pub.10.1007/978-1-4615-0755-0_3
7 sg:pub.10.1007/978-1-4615-0755-0_4
8 sg:pub.10.1007/978-3-319-50062-1_25
9 sg:pub.10.1007/bf00739571
10 sg:pub.10.1007/bf01190967
11 sg:pub.10.1007/bf02218586
12 sg:pub.10.1007/bf02219847
13 sg:pub.10.1007/bf02671553
14 sg:pub.10.1007/s10469-005-0016-x
15 sg:pub.10.1023/a:1010521410739
16 sg:pub.10.1023/a:1012516217265
17 https://doi.org/10.1002/malq.19550010205
18 https://doi.org/10.1002/malq.19940400407
19 https://doi.org/10.1016/s0049-237x(08)71260-6
20 https://doi.org/10.1016/s0049-237x(99)80030-5
21 https://doi.org/10.1017/jsl.2013.8
22 https://doi.org/10.1070/rm1965v020n04abeh001188
23 https://doi.org/10.1090/conm/257/04025
24 https://doi.org/10.1093/logcom/exu066
25 https://doi.org/10.2140/pjm.1986.122.319
26 schema:datePublished 2019-05
27 schema:datePublishedReg 2019-05-01
28 schema:description A major theme in the study of degree structures of all types has been the question of the decidability or undecidability of their first order theories. This is a natural and fundamental question that is an important goal in the analysis of these structures. In this paper, we study decidability for theories of upper semilattices that arise from the theory of numberings. We use the following approach: given a level of complexity, say Σα0, we consider the upper semilattice RΣα0 of all Σα0-computable numberings of all Σα0-computable families of subsets of N. We prove that the theory of the semilattice of all computable numberings is computably isomorphic to first order arithmetic. We show that the theory of the semilattice of all numberings is computably isomorphic to second order arithmetic. We also obtain a lower bound for the 1-degree of the theory of the semilattice of all Σα0-computable numberings, where α≥2 is a computable successor ordinal. Furthermore, it is shown that for any of the theories T mentioned above, the Π5-fragment of T is hereditarily undecidable. Similar results are obtained for the structure of all computably enumerable equivalence relations on N, equipped with composition.
29 schema:genre research_article
30 schema:inLanguage en
31 schema:isAccessibleForFree false
32 schema:isPartOf Nc3655bda4d424f62b9c6c774964eb94f
33 Nd24eed039cf04874b482be968ec992f6
34 sg:journal.1136186
35 schema:name Elementary theories and hereditary undecidability for semilattices of numberings
36 schema:pagination 485-500
37 schema:productId N56a1df189f67486dbdf3a6902745230b
38 N8ae4f9bb2d764c97800e04a074804623
39 Nb9343429e30e409f80a87347aa14a4e6
40 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107260582
41 https://doi.org/10.1007/s00153-018-0647-y
42 schema:sdDatePublished 2019-04-11T13:05
43 schema:sdLicense https://scigraph.springernature.com/explorer/license/
44 schema:sdPublisher N3523642e791a40879a22134e033d7efb
45 schema:url https://link.springer.com/10.1007%2Fs00153-018-0647-y
46 sgo:license sg:explorer/license/
47 sgo:sdDataset articles
48 rdf:type schema:ScholarlyArticle
49 N26f52d87d48d45f1a23d4912354fd38f rdf:first sg:person.07664647506.18
50 rdf:rest Ndb2355a2da5043cfaeaa80fd0f655c4d
51 N3523642e791a40879a22134e033d7efb schema:name Springer Nature - SN SciGraph project
52 rdf:type schema:Organization
53 N5082e2b37ea4484f98843753344f9ffb rdf:first sg:person.011333325747.16
54 rdf:rest N26f52d87d48d45f1a23d4912354fd38f
55 N56a1df189f67486dbdf3a6902745230b schema:name readcube_id
56 schema:value f106e8cbb053510248d64e1f30a2f2bf9564c1b257bf29002dcbf05557acf36c
57 rdf:type schema:PropertyValue
58 N8ae4f9bb2d764c97800e04a074804623 schema:name dimensions_id
59 schema:value pub.1107260582
60 rdf:type schema:PropertyValue
61 Nb9343429e30e409f80a87347aa14a4e6 schema:name doi
62 schema:value 10.1007/s00153-018-0647-y
63 rdf:type schema:PropertyValue
64 Nc3655bda4d424f62b9c6c774964eb94f schema:issueNumber 3-4
65 rdf:type schema:PublicationIssue
66 Nd24eed039cf04874b482be968ec992f6 schema:volumeNumber 58
67 rdf:type schema:PublicationVolume
68 Ndb2355a2da5043cfaeaa80fd0f655c4d rdf:first sg:person.012726266747.26
69 rdf:rest rdf:nil
70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
71 schema:name Mathematical Sciences
72 rdf:type schema:DefinedTerm
73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
74 schema:name Pure Mathematics
75 rdf:type schema:DefinedTerm
76 sg:grant.6741084 http://pending.schema.org/fundedItem sg:pub.10.1007/s00153-018-0647-y
77 rdf:type schema:MonetaryGrant
78 sg:journal.1136186 schema:issn 0933-5846
79 1432-0665
80 schema:name Archive for Mathematical Logic
81 rdf:type schema:Periodical
82 sg:person.011333325747.16 schema:affiliation https://www.grid.ac/institutes/grid.4605.7
83 schema:familyName Bazhenov
84 schema:givenName Nikolay
85 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011333325747.16
86 rdf:type schema:Person
87 sg:person.012726266747.26 schema:affiliation https://www.grid.ac/institutes/grid.77268.3c
88 schema:familyName Yamaleev
89 schema:givenName Mars
90 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012726266747.26
91 rdf:type schema:Person
92 sg:person.07664647506.18 schema:affiliation https://www.grid.ac/institutes/grid.428191.7
93 schema:familyName Mustafa
94 schema:givenName Manat
95 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07664647506.18
96 rdf:type schema:Person
97 sg:pub.10.1007/978-0-387-68546-5_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044684096
98 https://doi.org/10.1007/978-0-387-68546-5_2
99 rdf:type schema:CreativeWork
100 sg:pub.10.1007/978-1-4615-0755-0_2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031120463
101 https://doi.org/10.1007/978-1-4615-0755-0_2
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/978-1-4615-0755-0_3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040782755
104 https://doi.org/10.1007/978-1-4615-0755-0_3
105 rdf:type schema:CreativeWork
106 sg:pub.10.1007/978-1-4615-0755-0_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025812806
107 https://doi.org/10.1007/978-1-4615-0755-0_4
108 rdf:type schema:CreativeWork
109 sg:pub.10.1007/978-3-319-50062-1_25 schema:sameAs https://app.dimensions.ai/details/publication/pub.1087289194
110 https://doi.org/10.1007/978-3-319-50062-1_25
111 rdf:type schema:CreativeWork
112 sg:pub.10.1007/bf00739571 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025496460
113 https://doi.org/10.1007/bf00739571
114 rdf:type schema:CreativeWork
115 sg:pub.10.1007/bf01190967 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052370847
116 https://doi.org/10.1007/bf01190967
117 rdf:type schema:CreativeWork
118 sg:pub.10.1007/bf02218586 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032702944
119 https://doi.org/10.1007/bf02218586
120 rdf:type schema:CreativeWork
121 sg:pub.10.1007/bf02219847 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046038075
122 https://doi.org/10.1007/bf02219847
123 rdf:type schema:CreativeWork
124 sg:pub.10.1007/bf02671553 schema:sameAs https://app.dimensions.ai/details/publication/pub.1045623965
125 https://doi.org/10.1007/bf02671553
126 rdf:type schema:CreativeWork
127 sg:pub.10.1007/s10469-005-0016-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1023339347
128 https://doi.org/10.1007/s10469-005-0016-x
129 rdf:type schema:CreativeWork
130 sg:pub.10.1023/a:1010521410739 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007013493
131 https://doi.org/10.1023/a:1010521410739
132 rdf:type schema:CreativeWork
133 sg:pub.10.1023/a:1012516217265 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052873081
134 https://doi.org/10.1023/a:1012516217265
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1002/malq.19550010205 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002259044
137 rdf:type schema:CreativeWork
138 https://doi.org/10.1002/malq.19940400407 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051830997
139 rdf:type schema:CreativeWork
140 https://doi.org/10.1016/s0049-237x(08)71260-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047970994
141 rdf:type schema:CreativeWork
142 https://doi.org/10.1016/s0049-237x(99)80030-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030028047
143 rdf:type schema:CreativeWork
144 https://doi.org/10.1017/jsl.2013.8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029607701
145 rdf:type schema:CreativeWork
146 https://doi.org/10.1070/rm1965v020n04abeh001188 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058193782
147 rdf:type schema:CreativeWork
148 https://doi.org/10.1090/conm/257/04025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089204430
149 rdf:type schema:CreativeWork
150 https://doi.org/10.1093/logcom/exu066 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059876649
151 rdf:type schema:CreativeWork
152 https://doi.org/10.2140/pjm.1986.122.319 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069069055
153 rdf:type schema:CreativeWork
154 https://www.grid.ac/institutes/grid.428191.7 schema:alternateName Nazarbayev University
155 schema:name Department of Mathematics, School of Science and Technology, Nazarbayev University, 53, Qabanbaybatyr Avenue, 010000, Astana, Kazakhstan
156 rdf:type schema:Organization
157 https://www.grid.ac/institutes/grid.4605.7 schema:alternateName Novosibirsk State University
158 schema:name Novosibirsk State University, 2 Pirogova St., 630090, Novosibirsk, Russia
159 Sobolev Institute of Mathematics, 4 Acad. Koptyug Ave., 630090, Novosibirsk, Russia
160 rdf:type schema:Organization
161 https://www.grid.ac/institutes/grid.77268.3c schema:alternateName Kazan Federal University
162 schema:name Kazan Federal University, 18 Kremlevskaya Str., 420008, Kazan, Russia
163 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...