EXPANSIONS OF THE ORDERED ADDITIVE GROUP OF REAL NUMBERS BY TWO DISCRETE SUBGROUPS
نویسندگان
چکیده
منابع مشابه
Expansions of the Ordered additive Group of Real numbers by two discrete Subgroups
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, <,+,Z,Za) defines monadic second order logic of one...
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Expansions of Real Numbers
It was discovered some years ago that there exist non-integer real numbers q > 1 for which only one sequence (ci) of integers 0 ≤ ci < q satisfies the equality P ∞ i=1 ciq −i = 1. The set U of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation. For each fi...
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ژورنال
عنوان ژورنال: The Journal of Symbolic Logic
سال: 2016
ISSN: 0022-4812,1943-5886
DOI: 10.1017/jsl.2015.34