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Forking in Generic Structures(Study of definability in nonstandard models of arithmetic)
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Weakly o-minimal structures(Study of definability in nonstandard models of arithmetic)
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Nonstandard models that are definable in models of Peano Arithmetic
Mathematical Logic Quarterly, 2007AbstractIn this paper, we investigate definable models of Peano Arithmetic PA in a model of PA. For any definable model N without parameters in a model M, we show that N is isomorphic to M if M is elementary extension of the standard model and N is elementarily equivalent to M.
Akito Tsuboi
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Nonstandard Models for a Fragment of the Arithmetic and Their Decision Problem
Zeitschrift Für Mathematische Logik Und Grundlagen Der Mathematik, 1987In my thesis [see Bonner Math. Schriften 61 (1973; Zbl 0279.02039)] I have introduced the theory of Very Weak Induction for open formulae VWIO, which differs from WIO (AIO) studied by \textit{J. C. Shepherdson} [Bull. Acad. Pol. Sci., Ser. Sci. Math. Astron. Phys.
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Nonstandard models for arithmetic and analysis
Studia Logica, 1974Alexander Abian
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