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Preprint Number 755
755. Philipp Hieronymi
Expansions of the ordered additive group of real numbers by two discrete subgroups
Submission date: 25 July 2014.
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:
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