Peretyat’kin, Mikhail Finitely axiomatizable theories and Lindenbaum algebras of semantic classes. (English) Zbl 0968.03039 Cholak, Peter A. (ed.) et al., Computability theory and its applications. Current trends and open problems. Proceedings of a 1999 AMS-IMS-SIAM joint summer research conference, Boulder, CO, USA, June 13-17, 1999. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 257, 221-239 (2000). This is a survey on Lindenbaum algebras of elementary theories. A series of statements on Lindenbaum algebras of semantic classes of models is proved and a number of problems is formulated. In particular, the author proves the existence of universal Boolean algebras for some classes of arithmetical and analytical hierarchies.For the entire collection see [Zbl 0945.00017]. Reviewer: Andrei S.Morozov (Novosibirsk) Cited in 1 Document MSC: 03C57 Computable structure theory, computable model theory 03D45 Theory of numerations, effectively presented structures 03D55 Hierarchies of computability and definability 03G05 Logical aspects of Boolean algebras 03B10 Classical first-order logic Keywords:Lindenbaum algebra; universal Boolean algebra; finitely axiomatizable theory; survey PDFBibTeX XMLCite \textit{M. Peretyat'kin}, Contemp. Math. 257, 221--239 (2000; Zbl 0968.03039)