Degree spectra of real closed fields View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2019-05

AUTHORS

Russell Miller, Victor Ocasio González

ABSTRACT

Several researchers have recently established that for every Turing degree c, the real closed field of all c-computable real numbers has spectrum {d:d′≥c′′}. We investigate the spectra of real closed fields further, focusing first on subfields of the field R0 of computable real numbers, then on archimedean real closed fields more generally, and finally on non-archimedean real closed fields. For each noncomputable, computably enumerable set C, we produce a real closed C-computable subfield of R0 with no computable copy. Then we build an archimedean real closed field with no computable copy but with a computable enumeration of the Dedekind cuts it realizes, and a computably presentable nonarchimedean real closed field whose residue field has no computable presentation. More... »

PAGES

387-411

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00153-018-0638-z

DOI

http://dx.doi.org/10.1007/s00153-018-0638-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105740802


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