On Cofinal Submodels and Elementary Interstices

Notre Dame Journal of Formal Logic 53 (3):267-287 (2012)
  Copy   BIBTEX

Abstract

We prove a number of results concerning the variety of first-order theories and isomorphism types of pairs of the form $(N,M)$ , where $N$ is a countable recursively saturated model of Peano Arithmetic and $M$ is its cofinal submodel. We identify two new isomorphism invariants for such pairs. In the strongest result we obtain continuum many theories of such pairs with the fixed greatest common initial segment of $N$ and $M$ and fixed lattice of interstructures $K$ , such that $M\prec K\prec N$

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,635

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

On Cofinal Extensions of Models of Arithmetic.Henryk Kotlarski - 1983 - Journal of Symbolic Logic 48 (2):253-262.
Four Problems Concerning Recursively Saturated Models of Arithmetic.Roman Kossak - 1995 - Notre Dame Journal of Formal Logic 36 (4):519-530.
Elementary Cuts in Saturated Models of Peano Arithmetic.James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (1):1-13.
T-Convexity and Tame Extensions.LouDen Dries & Adam H. Lewenberg - 1995 - Journal of Symbolic Logic 60 (1):74 - 102.
Cofinal Extensions of Nonstandard Models of Arithmetic.C. Smoryński - 1981 - Notre Dame Journal of Formal Logic 22 (2):133-144.
On Cofinal Extensions of Models of Fragments of Arithmetic.Richard Kaye - 1991 - Notre Dame Journal of Formal Logic 32 (3):399-408.
Model-Theoretic Properties Characterizing Peano Arithmetic.Richard Kaye - 1991 - Journal of Symbolic Logic 56 (3):949-963.
Models with the Ω-Property.Roman Kossak - 1989 - Journal of Symbolic Logic 54 (1):177-189.
On Certain Types and Models for Arithmetic.Andreas Blass - 1974 - Journal of Symbolic Logic 39 (1):151-162.

Analytics

Added to PP
2012-09-25

Downloads
16 (#662,925)

6 months
1 (#419,510)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Roman Kossak
City University of New York

Citations of this work

Elementary Cuts in Saturated Models of Peano Arithmetic.James H. Schmerl - 2012 - Notre Dame Journal of Formal Logic 53 (1):1-13.

Add more citations

References found in this work

Models and Types of Peano's Arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
A Note on Satisfaction Classes.Roman Kossak - 1985 - Notre Dame Journal of Formal Logic 26 (1):1-8.
Arithmetically Saturated Models of Arithmetic.Roman Kossak & James H. Schmerl - 1995 - Notre Dame Journal of Formal Logic 36 (4):531-546.

View all 13 references / Add more references