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Diophantine theory of free inverse semigroups. (Russian) Zbl 0584.03005
An elementary sentence is diophantine if it has the following form: \(\exists x_ 1...x_ n\) \(F(x_ 1,...,x_ n)\) where \(F(x_ 1,...,x_ n)\) is a conjunction of atomic formulae. Let I denote a free inverse semigroup over a set A with at least two elements \(a_ 1\), \(a_ 2\). It is proved that any diophantine theory of I (i.e. any family of all diophantine sentences that hold in I) of signature \(<\cdot,^{-1},a_ 1,a_ 2>\) is undecidable.
Reviewer: M.Demlová

MSC:
03B25 Decidability of theories and sets of sentences
20M05 Free semigroups, generators and relations, word problems
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