On Some Uses of Nonstandard Models

• Autorzy: Kossak R.
• Języki publikacji: EN
• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2007
• Tom: Vol. 81, nr 1-3
• Strony: 165--172
• Opis fizyczny: bibliogr. 14 poz.

Twórcy

autor

Kossak R.

• The Graduate Center, City University of New York, 365 Fifth Avenue, Room 4208 New York, NY 10016-4309, USA,

Bibliografia

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• [2] Jin, R.: Nonstandard Analysis in Additive Number Theory, Bull. Symb. Logic, 6(3), 2000, 331-341.
• [3] Jin, R.: NonstandardMethods for Additive and Combinatorial Number Theory: A Survey, in: Proceedings of Conference on Non StandardMathematics, Aviero, Portugal, July 2004, Lecture Notes in Math., Association for Symbolic Logic, A K Peters, Ltd., 2006.
• [4] Keisler, H. J., Schmerl, J. H.: Making the hyperreal line both saturated and complete, J. Symbolic Logic, 56(3), 1991, 1016-1025, ISSN 0022-4812.
• [5] Kossak, R., Schmerl, J. H.: The Structure ofModels of Peano Arithmetic, Oxford Logic Guides 50, Clarendon Press, Oxford, 2006, ISBN 0-19-856827-4.
• [6] Kotlarski, H.: The incompleteness theorems after 70 years, Ann. Pure Appl. Logic, 126(1-3), 2004, 125-138.
• [7] Mac Dowell, R., Specker, E.: Modelle der Arithmetik, Pergamon, Oxford, 1961, 257-263.
• [8] Mostowski, A.: On models of axiomatic systems, Fund. Math., 39, 1953, 133-158.
• [9] Robinson, A.: On languageswhich are based on non-standard arithmetic, NagoyaMath. J., 22, 1963, 83-117.
• [10] Ryll-Nardzewski, C.: The role of the axiom of induction in elementary arithmetic., Fund. Math., 39, 1953, 239-263.
• [11] Schmerl, J. H.: Recursively saturated models generated by indiscernibles, Notre Dame J. Formal Logic, 26(2), 1985, 99-105, ISSN 0029-4527.
• [12] Schmerl, J. H.: Generic automorphisms and graph coloring, Discrete Math., 291(1-3), 2005, 235-242, ISSN 0012-365X.
• [13] Sheperdson, J. C.: A non-standard model for a free variable fragment of number theory, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 12, 1964, 79-86.
• [14] Tennenbaum, S.: Non-archimedean models for arithmetic, Notices Amer. Math. Soc., 6, 1959, 270.