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Weak theories of nonstandard arithmetic and analysis
Abstract
A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched.Author's Profile
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Citations of this work
A functional interpretation for nonstandard arithmetic.Benno van den Berg, Eyvind Briseid & Pavol Safarik - 2012 - Annals of Pure and Applied Logic 163 (12):1962-1994.
Number theory and elementary arithmetic.Jeremy Avigad - 2003 - Philosophia Mathematica 11 (3):257-284.
The Mathematical Intelligencer Flunks the Olympics.Alexander E. Gutman, Mikhail G. Katz, Taras S. Kudryk & Semen S. Kutateladze - 2017 - Foundations of Science 22 (3):539-555.
References found in this work
Metamathematical Investigation of Intuitionistic Arithmetic and Analysis.Anne S. Troelstra - 1973 - New York: Springer.
Mathematically strong subsystems of analysis with low rate of growth of provably recursive functionals.Ulrich Kohlenbach - 1996 - Archive for Mathematical Logic 36 (1):31-71.
A feasible theory for analysis.Fernando Ferreira - 1994 - Journal of Symbolic Logic 59 (3):1001-1011.
Interpreting classical theories in constructive ones.Jeremy Avigad - 2000 - Journal of Symbolic Logic 65 (4):1785-1812.
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