Undecidable semiassociative relation algebras

Journal of Symbolic Logic 59 (2):398-418 (1994)
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 Lwx is an undecidable theory. A stronger algebraic result shows that the set of logically valid sentences in Lwx forms a hereditarily undecidable theory in Lwx. These results generalize similar theorems, due to Tarski, concerning relation algebras and the formalism Lx
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