The strength of countable saturation

Archive for Mathematical Logic 56 (5-6):699-711 (2017)

Authors
Benno Van Den Berg
University of Amsterdam
Abstract
In earlier work we introduced two systems for nonstandard analysis, one based on classical and one based on intuitionistic logic; these systems were conservative extensions of first-order Peano and Heyting arithmetic, respectively. In this paper we study how adding the principle of countable saturation to these systems affects their proof-theoretic strength. We will show that adding countable saturation to our intuitionistic system does not increase its proof-theoretic strength, while adding it to the classical system increases the strength from first- to full second-order arithmetic.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
ISBN(s)
DOI 10.1007/s00153-017-0567-2
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 46,355
Through your library

References found in this work BETA

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.
The Syntax of Nonstandard Analysis.Edward Nelson - 1988 - Annals of Pure and Applied Logic 38 (2):123-134.

View all 10 references / Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

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.
Bounded Scott Set Saturation.Alex M. McAllister - 2002 - Mathematical Logic Quarterly 48 (2):245-259.
Automorphisms of Countable Short Recursively Saturated Models of PA.Erez Shochat - 2008 - Notre Dame Journal of Formal Logic 49 (4):345-360.
Countable Fréchetα 1-Spaces May Be First Countable.Alan Dow & Juris Stepräns - 1992 - Archive for Mathematical Logic 32 (1):33-50.
The Computational Strengths of Α-Tape Infinite Time Turing Machines.Benjamin Rin - 2014 - Annals of Pure and Applied Logic 165 (9):1501-1511.
End Extensions and Numbers of Countable Models.Saharon Shelah - 1978 - Journal of Symbolic Logic 43 (3):550-562.
A Complicated Ω-Stable Depth 2 Theory.Martin Koerwien - 2011 - Journal of Symbolic Logic 76 (1):47 - 65.
Unions and the Axiom of Choice.Omar de la Cruz, Eric Hall, Paul Howard, Kyriakos Keremedis & Jean Rubin - 2008 - Mathematical Logic Quarterly 54 (6):652-665.

Analytics

Added to PP index
2017-08-04

Total views
19 ( #484,789 of 2,286,122 )

Recent downloads (6 months)
6 ( #195,941 of 2,286,122 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature