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The theory of all substructures of a structure: Characterisation and decision problems1

Published online by Cambridge University Press:  12 March 2014

Kenneth L. Manders
Kenneth L. Manders*
Affiliation:
Group in Logic and Methodology of Science, University of California, Berkeley, California 94720
*
Department of Philosophy and Mathematics, University of Pittsburg, Pittsburg, PA 15260
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Abstract

An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure 〈R, ≤, + 〉 this gives a decision procedure for the ∃x∀y-part of the theory of all substructures, yet we show that the ∃x1x2∀y-part, and the entire theory, is Π11-complete. The theory of all ordered subsemigroups of 〈R, ≤, + 〉 is also shown Π11-complete. Applications in the philosophy of science are mentioned.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 44 , Issue 4 , December 1979 , pp. 583 - 598
Copyright
Copyright © Association for Symbolic Logic 1979

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Footnotes

1

This research is part of the author's Ph.D. thesis, Studies in applied logic, University of California, Berkeley, 1978.

References

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