Some Diophantine properties of ordered polynomial rings.

Title: Some Diophantine properties of ordered polynomial rings.
Identifier: AAI9969722
identifier: 9969722
Creator: Raffer, Sidney.
Contributor: Adviser: Attila Mate
Date: 2000
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: The language of ordered rings has symbols for the ring operations and order relation, and constant symbols for 0 and 1. An integer-valued polynomial is a polynomial with rational coefficients assuming integer values at all integer arguments. Open induction is the theory in the language of ordered rings consisting of the axioms for ordered rings and induction axioms for quantifier-free formulas.;It is shown that the set of universal consequences of open induction is axiomatized by the axioms for ordered rings together with the set of sentences asserting that no integer-valued polynomial assumes at any integer argument a value between zero and one.;It is shown that the theory Diophantine correct open induction consisting of open induction together with all universal statements true in the ordered ring of integers is axiomatized by all sentences in the language of ordered rings consisting of a string of universal quantifiers followed by a single existential quantifier followed by an open formula.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.