Philipp Hieronymi : Expansions of the ordered additive group of real numbers by two discrete subgroups

Posted by Dima Sinapova , part of the Logic Seminar.

At

March 18, 2014, 4 p.m.

In

SEO 427

Abstract

Let R be the set of real numbers and let Z be the set of integers. The theory (R,<,+,Z,aZ) is decidable if a is quadratic. If a is the golden ratio, (R,<,+,Z,aZ) defines multiplication by a. The results are established by using the Ostrowski representation of a real number based on the continued fraction expansions of a to define the above structures in monadic second order logic of one successor.