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Undecidable semiassociative relation algebras

Published online by Cambridge University Press:  12 March 2014

Roger D. Maddux
Roger D. Maddux*
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011-2066, E-mail: maddux@vincent.iastate.edu
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Abstract

If K is a class of semiassociative relation algebras and K contains the relation algebra of all binary relations on a denumerable set, then the word problem for the free algebra over K on one generator is unsolvable. This result implies that the set of sentences which are provable in the formalism ℒw × is an undecidable theory. A stronger algebraic result shows that the set of logically valid sentences in ℒw × forms a hereditarily undecidable theory in ℒw ×. These results generalize similar theorems, due to Tarski, concerning relation algebras and the formalism ℒ ×.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 2 , June 1994 , pp. 398 - 418
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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