Formalizing non-standard arguments in second-order arithmetic

Journal of Symbolic Logic 75 (4):1199-1210 (2010)
  Copy   BIBTEX

Abstract

In this paper, we introduce the systems ns-ACA₀ and ns-WKL₀ of non-standard second-order arithmetic in which we can formalize non-standard arguments in ACA₀ and WKL₀, respectively. Then, we give direct transformations from non-standard proofs in ns-ACA₀ or ns-WKL₀ into proofs in ACA₀ or WKL₀

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1286198143

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Formalizing forcing arguments in subsystems of second-order arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
Weak theories of nonstandard arithmetic and analysis.Jeremy Avigad - manuscript
Fundamental notions of analysis in subsystems of second-order arithmetic.Jeremy Avigad - 2006 - Annals of Pure and Applied Logic 139 (1):138-184.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Theories of arithmetics in finite models.Michał Krynicki & Konrad Zdanowski - 2005 - Journal of Symbolic Logic 70 (1):1-28.
Quantum Mathematics.J. Michael Dunn - 1980 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1980:512 - 531.
Witnessing functions in bounded arithmetic and search problems.Mario Chiari & Jan Krajíček - 1998 - Journal of Symbolic Logic 63 (3):1095-1115.
Could experience disconfirm the propositions of arithmetic?Jessica M. Wilson - 2000 - Canadian Journal of Philosophy 30 (1):55--84.
Syntactical truth predicates for second order arithmetic.Loïc Colson & Serge Grigorieff - 2001 - Journal of Symbolic Logic 66 (1):225-256.
Regularity in models of arithmetic.George Mills & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):272-280.
On the complexity of models of arithmetic.Kenneth McAloon - 1982 - Journal of Symbolic Logic 47 (2):403-415.
"True" arithmetic can prove its own consistency.Andrew Boucher -

Analytics

Added to PP
2010-09-12

Downloads
21 (#718,251)

6 months
10 (#251,846)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

A Nonstandard Counterpart of WWKL.Stephen G. Simpson & Keita Yokoyama - 2011 - Notre Dame Journal of Formal Logic 52 (3):229-243.
Ultrafilters in reverse mathematics.Henry Towsner - 2014 - Journal of Mathematical Logic 14 (1):1450001.
Nonstandard arithmetic and recursive comprehension.H. Jerome Keisler - 2010 - Annals of Pure and Applied Logic 161 (8):1047-1062.

Add more citations

References found in this work

Formalizing forcing arguments in subsystems of second-order arithmetic.Jeremy Avigad - 1996 - Annals of Pure and Applied Logic 82 (2):165-191.
Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Non‐standard Analysis in WKL 0.Kazuyuki Tanaka - 1997 - Mathematical Logic Quarterly 43 (3):396-400.

View all 7 references / Add more references