Submission date: 25 July 2014.

Abstract:

The theory of (R,<,+,Z,Z a) is decidable if a is quadratic. If a is the golden ratio, (R,<,+,Z,Z a) defines multiplication by a. The results are established by using the Ostrowski numeration system based on the continued fraction expansion of a to define the above structures in monadic second order logic of one successor. The converse that (R,<,+,Z,Z a) defines monadic second order logic of one successor, will also be established.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1407.7002: pdf, ps).