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UNDECIDABILITY OF THE THEORIES OF CLASSES OFSTRUCTURES

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 ofequivalence structures, and so on. Here, we study the (un)decidability of thetheory of several natural classes of structures with appropriate functions andrelations. For some of these classes of structures, the resulting theory isdecidable; for some of these classes of structures, the resulting theory isbi-interpretable with second-order arithmetic.

Keywords

bi-interpretabilitysecond-order arithmeticTarski’s Cube Problemclasses of structures

Information

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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