Second-order Non-nonstandard Analysis

作者: J. M. Henle

DOI: 10.1023/A:1025119317177

关键词:

摘要: Following [3], we build higher-order models of analysis resembling the frameworks nonstandard analysis. The are entirely canonical, constructed without Choice. Weak transfer principles developed and applied to topology, graph theory, measure theory. A Loeb-like is constructed.

参考文章(9)
P. A. Loeb, A. E. Hurd, An Introduction to Nonstandard Real Analysis ,(2011)
J. M. Henle, Non-nonstandard analysis: Real infinitesimals The Mathematical Intelligencer. ,vol. 21, pp. 67- 73 ,(1999) , 10.1007/BF03024834
Richard Rado, J. E. Littlewood, Lectures on the theory of functions The Mathematical Gazette. ,vol. 29, pp. 236- ,(1945) , 10.2307/3609271
Erik Palmgren, Developments in Constructive Nonstandard Analysis The Bulletin of Symbolic Logic. ,vol. 4, pp. 233- 272 ,(1998) , 10.2307/421031
Karel Hrbacek, Realism, nonstandard set theory, and large cardinals Annals of Pure and Applied Logic. ,vol. 109, pp. 15- 48 ,(2001) , 10.1016/S0168-0072(01)00039-2
Erik Palmgren, A constructive approach to nonstandard analysis Annals of Pure and Applied Logic. ,vol. 73, pp. 297- 325 ,(1995) , 10.1016/0168-0072(94)00030-7
Mauro Di Nasso, An axiomatic presentation of the nonstandard methods in mathematics Journal of Symbolic Logic. ,vol. 67, pp. 315- 325 ,(2002) , 10.2178/JSL/1190150046
Elliott Lieb, Michael Loss, Analysis Graduate Studies in Mathematics. ,vol. 14, ,(2001) , 10.1090/GSM/014
Robert Goldblatt, Lectures on the hyperreals ,(1998)