Groups whose universal theory is axiomatizable by quasi-identities
Copyright policy )Groups whose universal theory is axiomatizable by quasi-identities
A group \(G\) is called square-like if the universal theory of \(G\) coincides with that of its direct square \(G\times G\). It is shown that the class of square-like groups is first-order axiomatizable. A group \(G\) is said to be discriminating if and only if \(G\) discriminates \(G\times G\). The class of all discriminating groups is a proper not first-order axiomatizable subclass of all square-like groups.
- Fairfield University United States
330, Computer Sciences, quasivarieties, Model-theoretic algebra, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), axiomatizable classes, universal theories, 004, Quasivarieties and varieties of groups, Equational classes, universal algebra in model theory, Physical Sciences and Mathematics, discriminating groups, Applications of logic to group theory, square-like groups, Quasivarieties
330, Computer Sciences, quasivarieties, Model-theoretic algebra, Word problems, other decision problems, connections with logic and automata (group-theoretic aspects), axiomatizable classes, universal theories, 004, Quasivarieties and varieties of groups, Equational classes, universal algebra in model theory, Physical Sciences and Mathematics, discriminating groups, Applications of logic to group theory, square-like groups, Quasivarieties
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