Abstract
AbstractWe 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.
Publisher
Cambridge University Press (CUP)
Cited by
23 articles.
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1. Multi-level nonstandard analysis and the axiom of choice;Journal of Logic and Analysis;2024-07-03
2. Weak set theories in foundational debates;Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences;2023-04-10
3. Infinitesimal analysis without the Axiom of Choice;Annals of Pure and Applied Logic;2021-06
4. The strength of compactness in Computability Theory and Nonstandard Analysis;Annals of Pure and Applied Logic;2019-11
5. COMPUTABILITY THEORY, NONSTANDARD ANALYSIS, AND THEIR CONNECTIONS;The Journal of Symbolic Logic;2019-09-23