Nonstandard arithmetic and recursive comprehension |
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Authors: | H. Jerome Keisler |
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Affiliation: | Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, United States |
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Abstract: | First order reasoning about hyperintegers can prove things about sets of integers. In the author’s paper Nonstandard Arithmetic and Reverse Mathematics, Bulletin of Symbolic Logic 12 (2006) 100-125, it was shown that each of the “big five” theories in reverse mathematics, including the base theory , has a natural nonstandard counterpart. But the counterpart of has a defect: it does not imply the Standard Part Principle that a set exists if and only if it is coded by a hyperinteger. In this paper we find another nonstandard counterpart, , that does imply the Standard Part Principle. |
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Keywords: | 03B30 03F35 03H15 11U10 |
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