An Effective Conservation Result for Nonstandard Arithmetic

Mathematical Logic Quarterly 46 (1):17-24 (2000)
  Copy   BIBTEX

Abstract

We prove that a nonstandard extension of arithmetic is effectively conservative over Peano arithmetic by using an internal version of a definable ultrapower. By the same method we show that a certain extension of the nonstandard theory with a saturation principle has the same proof-theoretic strength as second order arithmetic, where comprehension is restricted to arithmetical formulas

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

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

Through your library

Similar books and articles

Nonstandard arithmetic and reverse mathematics.H. Jerome Keisler - 2006 - Bulletin of Symbolic Logic 12 (1):100-125.
Relative arithmetic.Sam Sanders - 2010 - Mathematical Logic Quarterly 56 (6):564-572.
Regularity in models of arithmetic.George Mills & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):272-280.
The arithmetic of cuts in models of arithmetic.Richard Kaye - 2013 - Mathematical Logic Quarterly 59 (4-5):332-351.
On some formalized conservation results in arithmetic.P. Clote, P. Hájek & J. Paris - 1990 - Archive for Mathematical Logic 30 (4):201-218.
Tennenbaum's Theorem and Unary Functions.Sakae Yaegasi - 2008 - Notre Dame Journal of Formal Logic 49 (2):177-183.
Nonstandard Models and Kripke's Proof of the Gödel Theorem.Hilary Putnam - 2000 - Notre Dame Journal of Formal Logic 41 (1):53-58.
On certain types and models for arithmetic.Andreas Blass - 1974 - Journal of Symbolic Logic 39 (1):151-162.

Analytics

Added to PP
2013-12-01

Downloads
14 (#846,545)

6 months
3 (#445,838)

Historical graph of downloads
How can I increase my downloads?

References found in this work

No references found.

Add more references