Countable Short Recursively Saturated Models of Arithmetic

Author

Erez Shochat, Graduate Center, City University of New YorkFollow

Date of Degree

2006

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Roman Kossak

Committee Members

Joel David Hamkins

Laurence Kirby

Hans Schoutens

Subject Categories

Mathematics

Abstract

Short recursively saturated models of arithmetic are exactly the elementary initial segments of recursively saturated models of arithmetic. Since any countable recursively saturated model of arithmetic has continuum many elementary initial segments which are already recursively saturated, we turn our attention to the (countably many) initial segments which are not recursively saturated. We first look at properties of countable short recursively saturated models of arithmetic and show that although these models cannot be cofinally resplendent (an expandability property slightly weaker than resplendency), these models have non-definable expansions which are still short recursively saturated.

Comments

Digital reproduction from the UMI microform.

Recommended Citation

Shochat, Erez, "Countable Short Recursively Saturated Models of Arithmetic" (2006). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1786