New Constructions of Satisfaction Classes

2015 ◽  
pp. 321-335 ◽  
Author(s):  
Ali Enayat ◽  
Albert Visser
Keyword(s):  
Satisfaction Classes

scholarly journals A note on satisfaction classes.

1985 ◽  
Vol 26 (1) ◽  
pp. 1-8 ◽  
Author(s):  
Roman Kossak
Keyword(s):  
Satisfaction Classes

scholarly journals A case for satisfaction classes: model theoretic vs axiomatic approaches to the notion of truth

2013 ◽  
Vol 19 ◽  
pp. 246-259
Author(s):  
А. Стролло
Keyword(s):  
Language Change ◽  
Expressive Power ◽  
Point Of View ◽  
Truth Predicate ◽  
Basic Question ◽  
General Point ◽  
Relevant Role ◽  
Complicated Model ◽  
Axiomatic Approaches ◽  
Satisfaction Classes

One of the basic question we can ask about truth in a formal setting is what, if anything, we gain when we have a truth predicate at disposal. For example, does the expressive power of a language change or does the proof strength of a theory increase? Satisfaction classes are often described as complicated model theoretic constructions unable to give useful information toward the notion of truth from a general point of view. Their import is narrowed to a dimension of pure technical utility and curiosity. Here I offer an application of satisfaction classes in order to show that they can have a relevant role in confronting proof theoretical equivalent theories of truth.

Jon Barwise and John Schlipf. On recursively saturated models of arithmetic. Model theory and algebra, A memorial tribute to Abraham Robinson, edited by D. H. Saracino and V. B. Weispfenning, Lecture notes in mathematics, vol. 498, Springer-Verlag, Berlin, Heidelberg, and New York, 1975, pp. 42–55. - Patrick Cegielski, Kenneth McAloon, and George Wilmers. Modèles récursivement saturés de l'addition et de la multiplication des entiers naturels. Logic Colloquium '80, Papers intended for the European summer meeting of the Association for Symbolic Logic, edited by D. van Dalen, D. Lascar, and T. J. Smiley, Studies in logic and the foundations of mathematics, vol. 108, North-Holland Publishing Company, Amsterdam, New York, and London, 1982, pp. 57–68. - Julia F. Knight. Theories whose resplendent models are homogeneous. Israel journal of mathematics, vol. 42 (1982), pp. 151–161. - Julia Knight and Mark Nadel. Expansions of models and Turing degrees. The journal of symbolic logic, vol. 47 (1982), pp. 587–604. - Julia Knight and Mark Nadel. Models of arithmetic and closed ideals. The journal of symbolic logic, vol. 47 no. 4 (for 1982, pub. 1983), pp. 833–840. - Henryk Kotlarski. On elementary cuts in models of arithmetic. Fundamenta mathematicae, vol. 115 (1983), pp. 27–31. - H. Kotlarski, S. Krajewski, and A. H. Lachlan. Construction of satisfaction classes for nonstandard models. Canadian mathematical bulletin—Bulletin canadien de mathématiques, vol. 24 (1981), pp. 283–293. - A. H. Lachlan. Full satisfaction classes and recursive saturation. Canadian mathematical bulletin—Bulletin canadien de mathématiques, pp. 295–297. - Leonard Lipshitz and Mark Nadel. The additive structure of models of arithmetic. Proceedings of the American Mathematical Society, vol. 68 (1978), pp. 331–336. - Mark Nadel. On a problem of MacDowell and Specker. The journal of symbolic logic, vol. 45 (1980), pp. 612–622. - C. Smoryński. Back-and-forth inside a recursively saturated model of arithmetic. Logic Colloquium '80, Papers intended for the European summer meeting of the Association for Symbolic Logic, edited by D. van Dalen, D. Lascar, and T. J. Smiley, Studies in logic and the foundations of mathematics, vol. 108, North-Holland Publishing Company, Amsterdam, New York, and London, 1982, pp. 273–278. - C. Smoryński and J. Stavi. Cofinal extension preserves recursive saturation. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7,1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 338–345. - George Wilmers. Minimally saturated models. Model theory of algebra and arithmetic, Proceedings of the Conference on Applications of Logic to Algebra and Arithmetic held at Karpacz, Poland, September 1–7, 1979, edited by L. Pacholski, J. Wierzejewski, and A. J. Wilkie, Lecture notes in mathematics, vol. 834, Springer-Verlag, Berlin, Heidelberg, and New York, 1980, pp. 370–380.

1987 ◽  
Vol 52 (1) ◽  
pp. 279-284
Author(s):  
J.-P. Ressayre
Keyword(s):  
New York ◽  
Model Theory ◽  
Foundations Of Mathematics ◽  
Symbolic Logic ◽  
Recursive Saturation ◽  
North Holland Publishing ◽  
Lecture Notes ◽  
Recursively Saturated ◽  
Satisfaction Classes ◽  
Models Of Arithmetic

Construction of Satisfaction Classes for Nonstandard Models

1981 ◽  
Vol 24 (3) ◽  
pp. 283-293 ◽  
Author(s):  
H. Kotlarski ◽  
S. Krajewski ◽  
A. H. Lachlan
Keyword(s):  
Peano Arithmetic ◽  
Truth Values ◽  
Nonstandard Models ◽  
Satisfaction Classes ◽  
Satisfaction Class

AbstractGiven a resplendent model for Peano arithmetic there exists a full satisfaction class over , i.e. an assignment of truth-values, to all closed formulas in the sense of with parameters from , which satisfies the usual semantic rules. The construction is based on the consistency of an appropriate system of -logic which is proved by an analysis of standard approximations of nonstandard formulas.

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