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- Title
On generalizing free algebras for a functor.
- Authors
Coumans, Dion C. S.; van Gool, Samuel J.
- Abstract
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).
- Subjects
FUNCTOR theory; GENERALIZATION; PARTIAL algebras; FREE algebras; RING theory; ALGEBRAIC equations
- Publication
Journal of Logic & Computation, 2013, Vol 23, Issue 3, p645
- ISSN
0955-792X
- Publication type
Article
- DOI
10.1093/logcom/exs016