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UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

Published online by Cambridge University Press:  12 December 2014

ASHER M. KACH  and
ANTONIO MONTALBÁN
ASHER M. KACH
Affiliation:
DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF CALIFORNIA, BERKELEY 5734 S. UNIVERSITY AVE. BERKELEY, CA 94720, USA E-mail: kach@math.uchicago.eduURL: www.math.uchicago.edu/~kach E-mail: antonio@math.uchicago.eduURL: www.math.uchicago.edu/~antonio
ANTONIO MONTALBÁN
Affiliation:
DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF CALIFORNIA, BERKELEY 5734 S. UNIVERSITY AVE. BERKELEY, CA 94720, USA E-mail: kach@math.uchicago.eduURL: www.math.uchicago.edu/~kach E-mail: antonio@math.uchicago.eduURL: www.math.uchicago.edu/~antonio
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Abstract

Many classes of structures have natural functions and relations on them: concatenation of linear orders, direct product of groups, disjoint union of equivalence structures, and so on. Here, we study the (un)decidability of the theory of several natural classes of structures with appropriate functions and relations. For some of these classes of structures, the resulting theory is decidable; for some of these classes of structures, the resulting theory is bi-interpretable with second-order arithmetic.

Keywords

bi-interpretabilitysecond-order arithmeticTarski’s Cube Problemclasses of structures
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1001 - 1019
Copyright
Copyright © The Association for Symbolic Logic 2014 

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References

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