Nonstandard Arithmetic and Reverse Mathematics

@article{citeulike:2856035, abstract = {We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.}, author = {Keisler, Jerome H. }, citeulike-article-id = {2856035}, doi = {10.2307/3515886}, journal = {The Bulletin of Symbolic Logic}, keywords = {library, nonstandard-analysis, reverse-mathematics}, number = {1}, pages = {100--125}, posted-at = {2008-06-02 09:16:17}, priority = {2}, publisher = {Association for Symbolic Logic}, title = {Nonstandard Arithmetic and Reverse Mathematics}, url = {http://dx.doi.org/10.2307/3515886}, volume = {12}, year = {2006} }

TY - JOUR ID - citeulike:2856035 L3 - citeulike-article-id:2856035 TI - Nonstandard Arithmetic and Reverse Mathematics JF - The Bulletin of Symbolic Logic VL - 12 IS - 1 SP - 100 EP - 125 PB - Association for Symbolic Logic N2 - We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic. KW - library KW - nonstandard-analysis KW - reverse-mathematics AU - Keisler, Jerome PY - 2006/// UR - http://dx.doi.org/10.2307/3515886 ER -