Ordinal Numbers View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1971

AUTHORS

Gaisi Takeuti , Wilson M. Zaring

ABSTRACT

The theory of ordinal numbers is essentially a theory of well ordered sets. For Cantor an ordinal number was “the general concept which results from (a well-ordered aggregate) M if we abstract from the nature of its elements while retaining their order of precedence ...” It was Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970), working independently, who removed Cantor’s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism. More... »

PAGES

32-48

Book

TITLE

Introduction to Axiomatic Set Theory

ISBN

978-0-387-05302-8
978-1-4684-9915-5

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-1-4684-9915-5_7

DOI

http://dx.doi.org/10.1007/978-1-4684-9915-5_7

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028946067


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": {
          "name": [
            "University of Illinois, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Takeuti", 
        "givenName": "Gaisi", 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "University of Illinois, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zaring", 
        "givenName": "Wilson M.", 
        "type": "Person"
      }
    ], 
    "datePublished": "1971", 
    "datePublishedReg": "1971-01-01", 
    "description": "The theory of ordinal numbers is essentially a theory of well ordered sets. For Cantor an ordinal number was \u201cthe general concept which results from (a well-ordered aggregate) M if we abstract from the nature of its elements while retaining their order of precedence ...\u201d It was Gottlob Frege (1848\u20131925) and Bertrand Russell (1872\u20131970), working independently, who removed Cantor\u2019s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism.", 
    "genre": "chapter", 
    "id": "sg:pub.10.1007/978-1-4684-9915-5_7", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": {
      "isbn": [
        "978-0-387-05302-8", 
        "978-1-4684-9915-5"
      ], 
      "name": "Introduction to Axiomatic Set Theory", 
      "type": "Book"
    }, 
    "name": "Ordinal Numbers", 
    "pagination": "32-48", 
    "productId": [
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/978-1-4684-9915-5_7"
        ]
      }, 
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "89e452b3f98df339f754a910fc8ca0db39bcdd3732651da7b67fcac6365b1127"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1028946067"
        ]
      }
    ], 
    "publisher": {
      "location": "New York, NY", 
      "name": "Springer New York", 
      "type": "Organisation"
    }, 
    "sameAs": [
      "https://doi.org/10.1007/978-1-4684-9915-5_7", 
      "https://app.dimensions.ai/details/publication/pub.1028946067"
    ], 
    "sdDataset": "chapters", 
    "sdDatePublished": "2019-04-15T20:49", 
    "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/v90/0000000001_0000000264/records_8690_00000049.jsonl", 
    "type": "Chapter", 
    "url": "http://link.springer.com/10.1007/978-1-4684-9915-5_7"
  }
]
 

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.10.1007/978-1-4684-9915-5_7'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-9915-5_7'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-9915-5_7'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/978-1-4684-9915-5_7'


 

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

65 TRIPLES      21 PREDICATES      26 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/978-1-4684-9915-5_7 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N97a150d245304205bdd952e234378bb6
4 schema:datePublished 1971
5 schema:datePublishedReg 1971-01-01
6 schema:description The theory of ordinal numbers is essentially a theory of well ordered sets. For Cantor an ordinal number was “the general concept which results from (a well-ordered aggregate) M if we abstract from the nature of its elements while retaining their order of precedence ...” It was Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970), working independently, who removed Cantor’s numbers from the realm of psychology. In 1903 Russell defined an ordinal number to be an equivalence class of well ordered sets under order isomorphism.
7 schema:genre chapter
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N40a8d8be80684416ae1b5fb2025cd5c8
11 schema:name Ordinal Numbers
12 schema:pagination 32-48
13 schema:productId N6556c07e312c4ae6a20e79c7fae8cd12
14 Nc00033de0ae0407a9c3fe8011180bc0b
15 Ne929f1f6cb10419fb27f112f85741229
16 schema:publisher N5bd368157a1d4e9c94a3ed72b36504f9
17 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028946067
18 https://doi.org/10.1007/978-1-4684-9915-5_7
19 schema:sdDatePublished 2019-04-15T20:49
20 schema:sdLicense https://scigraph.springernature.com/explorer/license/
21 schema:sdPublisher N661799d60af24e69aa963351c9e52fbd
22 schema:url http://link.springer.com/10.1007/978-1-4684-9915-5_7
23 sgo:license sg:explorer/license/
24 sgo:sdDataset chapters
25 rdf:type schema:Chapter
26 N2198615f5e744b9f80473e515464ed4a schema:name University of Illinois, USA
27 rdf:type schema:Organization
28 N40a8d8be80684416ae1b5fb2025cd5c8 schema:isbn 978-0-387-05302-8
29 978-1-4684-9915-5
30 schema:name Introduction to Axiomatic Set Theory
31 rdf:type schema:Book
32 N5bd368157a1d4e9c94a3ed72b36504f9 schema:location New York, NY
33 schema:name Springer New York
34 rdf:type schema:Organisation
35 N6556c07e312c4ae6a20e79c7fae8cd12 schema:name doi
36 schema:value 10.1007/978-1-4684-9915-5_7
37 rdf:type schema:PropertyValue
38 N661799d60af24e69aa963351c9e52fbd schema:name Springer Nature - SN SciGraph project
39 rdf:type schema:Organization
40 N8cf5e3bb31be4c37a15b8e9239399570 schema:name University of Illinois, USA
41 rdf:type schema:Organization
42 N97a150d245304205bdd952e234378bb6 rdf:first Ncb9ef88a77414d56aab60157b6341040
43 rdf:rest Nfd21b2ba4ba24840ab1fc895f9f72a47
44 Nc00033de0ae0407a9c3fe8011180bc0b schema:name dimensions_id
45 schema:value pub.1028946067
46 rdf:type schema:PropertyValue
47 Nc05afcd6ca5748c7a73c10910c888a2a schema:affiliation N2198615f5e744b9f80473e515464ed4a
48 schema:familyName Zaring
49 schema:givenName Wilson M.
50 rdf:type schema:Person
51 Ncb9ef88a77414d56aab60157b6341040 schema:affiliation N8cf5e3bb31be4c37a15b8e9239399570
52 schema:familyName Takeuti
53 schema:givenName Gaisi
54 rdf:type schema:Person
55 Ne929f1f6cb10419fb27f112f85741229 schema:name readcube_id
56 schema:value 89e452b3f98df339f754a910fc8ca0db39bcdd3732651da7b67fcac6365b1127
57 rdf:type schema:PropertyValue
58 Nfd21b2ba4ba24840ab1fc895f9f72a47 rdf:first Nc05afcd6ca5748c7a73c10910c888a2a
59 rdf:rest rdf:nil
60 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
61 schema:name Mathematical Sciences
62 rdf:type schema:DefinedTerm
63 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
64 schema:name Pure Mathematics
65 rdf:type schema:DefinedTerm
 




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


...