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ON THE ARITHMETICAL COMPLEXITY OF MODELS

Part of: Computability and recursion theory Model theory General logic

Published online by Cambridge University Press:  10 October 2025

WARREN GOLDFARB Open the ORCID record for WARREN GOLDFARB [Opens in a new window]
WARREN GOLDFARB*
Affiliation:
HARVARD UNIVERSITY USA
*
E-mail: goldfarb@fas.harvard.edu
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Abstract

A recursive set of formulas of first-order logic with finitely many predicate letters, including “=”, has a model over the integers in which the predicates are Boolean combinations of recursively enumerable sets, if it has an infinite model at all. The proof corrects a fallacious argument published by Hensel and Putnam in 1969.

Keywords

first-order logicelementary model theoryrecursive enumerablecomplexity

MSC classification

Primary: 03B10: Classical first-order logic 03C68: Other classical first-order model theory 03D30: Other degrees and reducibilities

Information

Type
Article
Information
Bulletin of Symbolic Logic , First View , pp. 1 - 10
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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