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Unifying the model theory of first-order and second-order arithmetic via WKL*_0

Journal article
Authors Ali Enayat
Tin Lok Wong
Published in Annals of Pure and Applied Logic
Volume 30
Issue 6
Pages 1247-1283
ISSN 0168-0072
Publication year 2017
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 1247-1283
Language en
Keywords Nonstandard models, first order arithmetic, second order arithmetic
Subject categories Algebra and Logic, Mathematics, Logic


We develop machinery to make the Arithmetized Completeness Theorem more effective in the study of many models of IΔ0+BΣ1+exp, including all countable ones, by passing on to the conservative extension View the MathML source of IΔ0+BΣ1+exp. Our detailed study of the model theory of View the MathML source leads to the simplification and improvement of many results in the model theory of Peano arithmetic and its fragments pertaining to the construction of various types of end extensions and initial segments.

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