David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 52 (3):842-863 (1987)
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
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Stuart T. Smith (1989). Nonstandard Definability. Annals of Pure and Applied Logic 42 (1):21-43.
Similar books and articles
Petr Andreev & Karel Hrbacek (2004). Standard Sets in Nonstandard Set Theory. Journal of Symbolic Logic 69 (1):165-182.
Alessandro Berarducci & Margarita Otero (1996). A Recursive Nonstandard Model of Normal Open Induction. Journal of Symbolic Logic 61 (4):1228-1241.
Mauro Di Nasso (1998). Pseudo-Superstructures as Nonstandard Universes. Journal of Symbolic Logic 63 (1):222 - 236.
C. Ward Henson, Matt Kaufmann & H. Jerome Keisler (1984). The Strength of Nonstandard Methods in Arithmetic. Journal of Symbolic Logic 49 (4):1039-1058.
Jeremy Avigad & Jeffrey Helzner (2002). Transfer Principles in Nonstandard Intuitionistic Arithmetic. Archive for Mathematical Logic 41 (6):581-602.
Vladimir Kanovei & Michael Reeken (1998). Elementary Extensions of External Classes in a Nonstandard Universe. Studia Logica 60 (2):253-273.
H. Jerome Keisler (2006). Nonstandard Arithmetic and Reverse Mathematics. Bulletin of Symbolic Logic 12 (1):100-125.
Kenneth McAloon (1982). On the Complexity of Models of Arithmetic. Journal of Symbolic Logic 47 (2):403-415.
Mauro Di Nasso (2002). An Axiomatic Presentation of the Nonstandard Methods in Mathematics. Journal of Symbolic Logic 67 (1):315 - 325.
Added to index2009-01-28
Total downloads11 ( #219,154 of 1,727,148 )
Recent downloads (6 months)1 ( #369,877 of 1,727,148 )
How can I increase my downloads?