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  1. Strong and Weak Truth Principles.Bartosz Wcisło Mateusz Łełyk - 2017 - Studia Semiotyczne—English Supplement 29:107-126.
    This paper is an exposition of some recent results concerning various notions of strength and weakness of the concept of truth, both published or not. We try to systematically present these notions and their relationship to the current research on truth. We discuss the concept of the Tarski boundary between weak and strong theories of truth and we give an overview of non-conservativity results for the extensions of the basic compositional truth theory. Additionally, we present a natural strong theory of (...)
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  • Models of expansions of equation image with no end extensions.Saharon Shelah - 2011 - Mathematical Logic Quarterly 57 (4):341-365.
    We deal with models of Peano arithmetic. The methods are from creature forcing. We find an expansion of equation image such that its theory has models with no end extensions. In fact there is a Borel uncountable set of subsets of equation image such that expanding equation image by any uncountably many of them suffice. Also we find arithmetically closed equation image with no ultrafilter on it with suitable definability demand. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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  • Interstitial and pseudo gaps in models of Peano Arithmetic.Ermek S. Nurkhaidarov - 2010 - Mathematical Logic Quarterly 56 (2):198-204.
    In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic M is a maximal subgroup of Aut if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a (...)
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  • Decoding in the automorphism group of a recursively saturated model of arithmetic.Ermek Nurkhaidarov - 2015 - Mathematical Logic Quarterly 61 (3):179-188.
    The main result of this paper partially answers a question raised in about the existence of countable just recursively saturated models of Peano Arithmetic with non‐isomorphic automorphism groups. We show the existence of infinitely many countable just recursively saturated models of Peano Arithmetic such that their automorphism groups are not topologically isomorphic. We also discuss maximal open subgroups of the automorphism group of a countable arithmetically saturated model of in a very good interstice.
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  • Definability of Initial Segments.Akito Tsuboi & Saharon Shelah - 2002 - Notre Dame Journal of Formal Logic 43 (2):65-73.
    In any nonstandard model of Peano arithmetic, the standard part is not first-order definable. But we show that in some model the standard part is definable as the unique solution of a formula , where P is a unary predicate variable.
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