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THERE ARE NO INTERMEDIATE STRUCTURES BETWEEN THE GROUP OF INTEGERS AND PRESBURGER ARITHMETIC

Published online by Cambridge University Press:  01 May 2018

GABRIEL CONANT
GABRIEL CONANT*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NOTRE DAME NOTRE DAME, IN46656, USAE-mail:gconant@nd.edu
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Abstract

We show that if a first-order structure ${\cal M}$, with universe ℤ, is an expansion of (ℤ,+,0) and a reduct of (ℤ,+,<,0), then ${\cal M}$ must be interdefinable with (ℤ ,+,0) or (ℤ ,+,<,0).

Keywords

Primary 03C6403C0706F20Secondary 03C45Presburger arithmeticexpansions of the group of integersdp-minimality
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 187 - 207
Copyright
Copyright © The Association for Symbolic Logic 2018 

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