Pinus, Aleksandr G. Some applications of infinitary logical languages in universal algebra. (English) Zbl 1305.08002 Math. Appl., Brno 2, No. 1, 93-103 (2013). 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 Keywords:infinite logical languages; universal algebras; geometric equivalence of algebras; Galois theory; Hamiltonian algebras PDFBibTeX XMLCite \textit{A. G. Pinus}, Math. Appl., Brno 2, No. 1, 93--103 (2013; Zbl 1305.08002) Full Text: DOI