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On decidability of the decomposability problem for finite theories

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Abstract

We consider the decomposability problem for elementary theories, i.e. the problem of deciding whether a theory has a nontrivial representation as a union of two (or several) theories in disjoint signatures. For finite universal Horn theories, we prove that the decomposability problem is \( \sum _1^0 \)-complete and, thus, undecidable. We also demonstrate that the decomposability problem is decidable for finite theories in signatures consisting only of monadic predicates and constants.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Andrey S. Morozov

  2. Institute of Informatics Systems, Novosibirsk, Russia

    Denis K. Ponomaryov

Authors
  1. Andrey S. Morozov
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  2. Denis K. Ponomaryov
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Corresponding author

Correspondence to Andrey S. Morozov.

Additional information

Original Russian Text Copyright © 2010 Morozov A. S. and Ponomaryov D. K.

The authors were supported by the Russian Foundation for Basic Research (Grant 05-01-04003-NNIO_a) and DFG project COMO, GZ: 436 RUS 113/829/0-1.

Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 4, pp. 838–847, July–August, 2010.

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Morozov, A.S., Ponomaryov, D.K. On decidability of the decomposability problem for finite theories. Sib Math J 51, 667–674 (2010). https://doi.org/10.1007/s11202-010-0068-6

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  • DOI: https://doi.org/10.1007/s11202-010-0068-6

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