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Some applications of infinitary logical languages in universal algebra. (English) Zbl 1305.08002

Summary: Some examples are given of applications of an infinite logical language in universal algebra, in the algebraic geometry of universal algebras, in the theory of implicit operations on algebras, in the Galois theory between automorphisms of universal algebras and its subalgebras of fixed points, in the theory of Hamiltonian closure of subalgebras and other areas.

MSC:

08A05 Structure theory of algebraic structures
08B05 Equational logic, Mal’tsev conditions
08-02 Research exposition (monographs, survey articles) pertaining to general algebraic systems
03C75 Other infinitary logic
03B25 Decidability of theories and sets of sentences
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