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REVERSE MATHEMATICS OF FIRST-ORDER THEORIES WITH FINITELY MANY MODELS

Published online by Cambridge University Press:  18 August 2014

DAVID R. BELANGER
DAVID R. BELANGER*
Affiliation:
DEPARTMENT OF MATHEMATICS CORNELL UNIVERSITY ITHACA, NY 14850-4201, USAE-mail: dbelanger@math.cornell.edu
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Abstract

We examine the reverse-mathematical strength of several theorems in classical and effective model theory concerning first-order theories and their number of models. We prove that, among these, most are equivalent to one of the familiar systems RCA0, WKL0, or ACA0. We are led to a purely model-theoretic statement that implies WKL0 but refutes ACA0 over RCA0.

Keywords

Primary 03B3003C57Secondary 03C35number of modelsreverse mathematicseffective model theory
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 3 , September 2014 , pp. 955 - 984
Copyright
Copyright © The Association for Symbolic Logic 2014 

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