Elementary theories of completely simple semigroups |
| |
Authors: | Bella V. Rozenblat |
| |
Affiliation: | (1) Department of Mathematics, Department of Computer Science, Ben-Gurion University of the Negev, POB 653, 84105 Beer-Sheva, Israel |
| |
Abstract: | The connections between first-order formulas over a completely simple semigroupC and corresponding formulas over its structure groupH are found in this paper. For the case of finite sandwich-matrix the criterion of decidability of the elementary theoryT(C) is established in terms of the elementary theory ofH in the enriched signature (Theorem 1). For the general case the criterion is established in terms of two-sorted algebraic systems (Theorem 2). Sufficient conditions in terms ofH for decidability and for undecidability ofT(C) are outlined. Corollaries and examples are presented, among them an example of a completely simple semigroup with a finite structure group and with undecidable elementary theory (Theorem 3). |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|