Louise Hay Logic Seminar
Demirhan Tunc
Notre Dame
Expansions of Presburger Arithmetic
Abstract: I will start with discussing decidability and undecidability results about expansions of Presburger Arithmetic, the first order theory of integers with addition. I will then describe how the real field with two small multiplicative groups gives rise to such an expansion and how we might approach this structure for obtaining a decidability result.
References:
[1] Bies A., A survey of arithmetical definability, A tribute to Maurice Boa, Bull. Belg. Math. Soc. Simon
Stevin 2001, suppl., 1-54.
[2] Point F., On decidable extensions of Presburger arithmetic: from A. Bertrand numeration systems to
Pisot numbers, Journal of Symbolic Logic, volume 65, number 3, 2000.
[3] Point, F., On the expansion (N;+; 2x) of Presburger arithmetic, To appear in Boolean Relation Theory
and Incompleteness, http://www.math.ohio-state.edu/friedman/manuscripts.html
[4] van den Dries, L., Gunaydin, A., The fields of real and complex numbers with a small multiplicative
group, Proc. London Math. Soc. (3), 93, 2006, no. 1, 43-81.
There will be Tea to start. There will be a party following the seminar, at the organizer's house.
Thursday April 29, 2010 at 3:00 PM in SEO 612