Journal of Symbolic Logic 56 (3):949-963 (1991)

Abstract
Let $\mathscr{L} = \{0, 1, +, \cdot, <\}$ be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order $\mathscr{L}$-theory containing $I\Delta_0 + \exp$ such that every complete extension $T$ of it has a countable model $K$ satisfying. $K$ has no proper elementary substructures, and whenever $L \prec K$ is a countable elementary extension there is $\bar{L} \prec L$ and $\bar{K} \subseteq_\mathrm{e} \bar{L}$ such that $K \prec_{\mathrm{cf}}\bar{K}$. Other model-theoretic conditions similar to and are also discussed and shown to characterize Peano arithmetic.
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2275063
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 63,339
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

On Cofinal Extensions of Models of Fragments of Arithmetic.Richard Kaye - 1991 - Notre Dame Journal of Formal Logic 32 (3):399-408.

Add more references

Citations of this work BETA

The Theory of $\kappa$ -Like Models of Arithmetic.Richard Kaye - 1995 - Notre Dame Journal of Formal Logic 36 (4):547-559.

Add more citations

Similar books and articles

Model-Theoretic Properties Characterizing Peano Arithmetic.Richard Kaye - 1991 - Journal of Symbolic Logic 56 (3):949-963.
Generic Cuts in Models of Arithmetic.Richard Kaye - 2008 - Mathematical Logic Quarterly 54 (2):129-144.
A Model of Peano Arithmetic with No Elementary End Extension.George Mills - 1978 - Journal of Symbolic Logic 43 (3):563-567.
Interstitial and Pseudo Gaps in Models of Peano Arithmetic.Ermek S. Nurkhaidarov - 2010 - Mathematical Logic Quarterly 56 (2):198-204.
Models Without Indiscernibles.Fred G. Abramson & Leo A. Harrington - 1978 - Journal of Symbolic Logic 43 (3):572-600.
Torre Models in the Isols.Joseph Barback - 1994 - Journal of Symbolic Logic 59 (1):140-150.
On the Complexity of Models of Arithmetic.Kenneth McAloon - 1982 - Journal of Symbolic Logic 47 (2):403-415.
The Theory of $\kappa$ -Like Models of Arithmetic.Richard Kaye - 1995 - Notre Dame Journal of Formal Logic 36 (4):547-559.
An Effective Conservation Result for Nonstandard Arithmetic.Erik Palmgren - 2000 - Mathematical Logic Quarterly 46 (1):17-24.
Fixed Points in Peano Arithmetic with Ordinals.Gerhard Jäger - 1993 - Annals of Pure and Applied Logic 60 (2):119-132.

Analytics

Added to PP index
2016-06-30

Total views
7 ( #1,037,876 of 2,448,744 )

Recent downloads (6 months)
1 ( #445,251 of 2,448,744 )

How can I increase my downloads?

Downloads

My notes