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Equivalents for a Quasivariety to be Generated by a Single Structure |
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| Authors: | W. Dziobiak A. V. Kravchenko P. J. Wojciechowski |
| Affiliation: | (1) Department of Mathematical Sciences, University of Puerto Rico, Mayagüez Campus, Mayagüez, PR 00681–9018, USA;(2) Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia;(3) Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX 79968–0514, USA |
| Abstract: | We present some equivalent conditions for a quasivariety  of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if  are nontrivial, then there exists  such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in  is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5]. Presented by Jacek Malinowski |
| Keywords: | Quasivariety embedding property Ł oś – Suszko rule free product generation by a single structure |
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