Diophantine Correct Open Induction

Details Diophantine Correct Open Induction Diophantine Correct Open Induction

2010-10-19

arxiv.org/abs/1010.3798v1

Mathematics

Logic

16 pages. To be published in "Set theory, Arithmetic, Philosophy: Essays in Memory of Stanley Tennenbaum (edited by J. Kennedy

Scientific paper

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.

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