On generalizing free algebras for a functor

In this article we introduce a new setting, based on partial algebras, for studying constructions of finitely generated free algebras. We give sufficient conditions under which the finitely generated free algebras for a variety V may be described as the colimit of a chain of finite partial algebras...

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Bibliographic Details
Published in:Journal of logic and computation 2013-06, Vol.23 (3), p.645-672
Main Authors: Coumans, D. C. S., van Gool, S. J.
Format: Article
Language:English
Subjects:
Algebra
Chains
Computation
Construction
Logic
Mathematical analysis
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Summary:In this article we introduce a new setting, based on partial algebras, for studying constructions of finitely generated free algebras. We give sufficient conditions under which the finitely generated free algebras for a variety V may be described as the colimit of a chain of finite partial algebras obtained by repeated application of a functor. In particular, our method encompasses the construction of finitely generated free algebras for varieties of algebras for a functor as in Bezhanishvili and Kurz (2007, LNCS, 143-157), Heyting algebras as in Bezhanishvili and Gehrke (2011, LMCS, 7, 1-24) and S4 algebras as in Ghilardi (2010, J. Appl. Non-classical, Logics, 20, 193-217).
ISSN:0955-792X
1465-363X
DOI:10.1093/logcom/exs016