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EXPANSIONS OF THE ORDERED ADDITIVE GROUP OF REAL NUMBERS BY TWO DISCRETE SUBGROUPS

Published online by Cambridge University Press:  10 May 2016

PHILIPP HIERONYMI
PHILIPP HIERONYMI*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN 1409 WEST GREEN STREET URBANA, IL 61801, USAE-mail: phierony@illinois.eduURL: http://www.math.uiuc.edu/∼phierony
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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.

Keywords

ordered additive group of real numbersdecidabilityOstrowski numeration systemmonadic second order logic of one successor
Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 3 , September 2016 , pp. 1007 - 1027
Copyright
Copyright © The Association for Symbolic Logic 2016 

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