Nonstandard characterizations of recursive saturation and resplendency

Journal of Symbolic Logic 52 (3):842-863 (1987)
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Abstract

We prove results about nonstandard formulas in models of Peano arithmetic which complement those of Kotlarski, Krajewski, and Lachlan in [KKL] and [L]. This enables us to characterize both recursive saturation and resplendency in terms of statements about nonstandard sentences. Specifically, a model M of PA is recursively saturated iff M is nonstandard and M-logic is consistent.M is resplendent iff M is nonstandard, M-logic is consistent, and every sentence φ which is consistent in M-logic is contained in a full satisfaction class for M. Thus, for models of PA, recursive saturation can be expressed by a (standard) Σ 1 1 -sentence and resplendency by a ▵ 1 2 -sentence

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Citations of this work

Nonstandard Definability.Stuart T. Smith - 1989 - Annals of Pure and Applied Logic 42 (1):21-43.
Truth, Pretense and the Liar Paradox.Bradley Armour-Garb & James A. Woodbridge - 2015 - In Kentaro Fujimoto, José Martínez Fernández, Henri Galinon & Theodora Achourioti (eds.), Unifying the Philosophy of Truth. Springer Verlag. pp. 339-354.

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References found in this work

Factorization of Polynomials and °1 Induction.S. G. Simpson - 1986 - Annals of Pure and Applied Logic 31:289.

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