On embedding models of arithmetic into reduced powers.

Title: On embedding models of arithmetic into reduced powers.
Identifier: AAI9630472
identifier: 9630472
Creator: Kennedy, Juliette Cara.
Contributor: Adviser: Attila Mate
Date: 1996
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In the early 1970's Tennenbaum proved that countable non-standard models of PA--which are Diophantine correct are all present up to isomorphism in a reduced power of the integers modulo the co-finite filter. This allows one to translate questions about models of arithmetic into questions about the structure of this reduced power. In particular, the statement that the MRDP theorem is provable in a given discretely ordered semi-ring has as equivalents a number of elementary statements about the coordinatewise behavior of {dollar}\Delta\sb0{dollar} formulas in the reduced power. We have also given characterizations of various fragments of arithmetic theories in terms of coordinatewise behavior of formulas, and in terms of cohesiveness properties.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.