Expansions of the ordered additive group of real numbers by two discrete subgroups

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Abstract

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 successor, will also be established.

Original languageEnglish (US)
Pages (from-to)1007-1027
Number of pages21
JournalJournal of Symbolic Logic
Volume81
Issue number3
DOIs
StatePublished - Sep 1 2016

Keywords

  • Decidability
  • Monadic second order logic of one successor
  • Ordered additive group of real numbers
  • Ostrowski numeration system

ASJC Scopus subject areas

  • Philosophy
  • Logic

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