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- W2070926400 abstract "We survey results and problems concerning subsystems of Peano Arithmetic. In particular, we deal with end extensions of models of such theories. First, we discuss the results of Paris and Kirby (Logic Colloquium ’77, North-Holland, Amsterdam, 1978, pp. 199–209) and of Clote (Fund. Math. 127 (1986) 163; Fund. Math. 158 (1998) 301), which generalize the MacDowell and Specker theorem (Proc. Symp. on Foundation of Mathematics, Warsaw, 1959, Pergamon Press, Oxford, 1961, p. 257–263) we also discuss a related problem of Kaufmann (On existence of Σ n end extensions, Lecture Notes in Mathematics, Vol. 859, Springer, Berlin, 1980, pp. 92). Then we sketch an alternative proof of Clote's theorem, using the arithmetized completeness theorem in the spirit of McAloon (Trans. Amer. Math. Soc. 239 (1978) 253) and Paris (Some conservation results for fragments of arithmetic, Lecture Notes in Mathematics, Vol. 890, Springer, Berlin, 1981, p. 251)." @default.
- W2070926400 created "2016-06-24" @default.
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- W2070926400 date "2001-04-01" @default.
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- W2070926400 title "On end extensions of models of subsystems of peano arithmetic" @default.
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- W2070926400 doi "https://doi.org/10.1016/s0304-3975(00)00110-9" @default.
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