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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].

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
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