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UNDECIDABILITY OF THE THEORIES OF CLASSES OF STRUCTURES

Published online by Cambridge University Press:  12 December 2014

ASHER M. KACH
Affiliation:
DEPARTMENT OF MATHEMATICS THE UNIVERSITY OF CALIFORNIA, BERKELEY 5734 S. UNIVERSITY AVE. BERKELEY, CA 94720, USA E-mail: [email protected]: www.math.uchicago.edu/~kach E-mail: [email protected]: 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: [email protected]: www.math.uchicago.edu/~kach E-mail: [email protected]: www.math.uchicago.edu/~antonio

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.

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2014 

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References

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