Philipp Hieronymi

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The theory of (R, <, +, Z, Za) is decidable if a is quadratic. If a is the golden ratio, (R, <, +, Z, Za) 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, <, +,(More)
A Cantor set is a non-empty, compact set that has neither interior nor isolated points. In this paper a Cantor set K ⊆ R is constructed such that every set definable in (R, <, +, ·, K) is Borel. In addition, we prove quantifier-elimination and completeness results for (R, <, +, ·, K), making the set K the first example of a modeltheoretically tame Cantor(More)