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Preprint Number 1153
1153. William Balderrama, Philipp Hieronymi Definability and decidability in expansions by generalized Cantor
sets E-mail: Submission date: 29 January 2017 Abstract: We determine the sets definable in expansions of the ordered real additive
group by generalized Cantor sets. Given a natural number r ≥ 3, we say a
set C is a generalized Cantor set in base r if there is a non-empty
K ⊆ {1,...,r-2} such that C is the set of those numbers in
[0,1] that admit a base r expansion omitting the digits in K. Mathematics Subject Classification: Primary 03B25 Secondary 03B70, 03C64, 28A80 Keywords and phrases: |

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