REVERSE MATHEMATICS OF FIRST-ORDER THEORIES WITH FINITELY MANY MODELS-Reference-Cited by-同舟云学术

REVERSE MATHEMATICS OF FIRST-ORDER THEORIES WITH FINITELY MANY MODELS

Published:2014-08-18 Issue:3 Volume:79 Page:955-984
ISSN:0022-4812
Container-title:The Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

BELANGER DAVID R.

Abstract

AbstractWe 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference24 articles.

1. [4] Engeler Erwin , Äquivalenzklassen von n-Tupeln. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik , vol. 5 (1959), pp. 340–345.

2. [3] Ehrenfeucht Andrzej , Separable theories. Bulletin L’Académie Polonaise des Science, Série des Sciences Mathématiques, Astronomiques et Physiques , vol. 9 (1961), pp. 17–19.

3. [13] Hirschfeldt Denis R. , Shore Richard A. , and Slaman Theodore A. , The atomic model theorem and type omitting. Transactions of the American Mathematical Society , vol. 361 (2009), no. 11, pp. 5805–5837.

4. [19] Peretjat´kin Mikhail G. , A criterion for strong constructivizability of a homogeneous model. Algebra i Logika , vol. 17 (1978), no. 4, pp. 436–454.

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