Diophantine Correct Open Induction
Logic
2010-10-20 v1
Abstract
We give an induction-free axiom system for diophantine correct open induction. We relate the problem of whether a finitely generated ring of Puiseux polynomials is diophantine correct to a problem about the value-distribution of a tuple of semialgebraic functions with integer arguments. We use this result, and a theorem of Bergelson and Leibman on generalized polynomials, to identify a class of diophantine correct subrings of the field of descending Puiseux series with real coefficients.
Keywords
Cite
@article{arxiv.1010.3798,
title = {Diophantine Correct Open Induction},
author = {Sidney Raffer},
journal= {arXiv preprint arXiv:1010.3798},
year = {2010}
}
Comments
16 pages. To be published in "Set theory, Arithmetic, Philosophy: Essays in Memory of Stanley Tennenbaum (edited by J. Kennedy and R. Kossak), Cambridge University Press."