Author:
Freytes Hector,Sergioli Giuseppe
Abstract
AbstractIn the framework of algebras with infinitary operations, the equational theory of $$\bigvee _{\kappa }$$
⋁
κ
-complete Heyting algebras or Heyting $$\kappa $$
κ
-frames is studied. A Hilbert style calculus algebraizable in this class is formulated. Based on the infinitary structure of Heyting $$\kappa $$
κ
-frames, an equational type completeness theorem related to the $$\langle \bigvee , \wedge , \rightarrow , 0 \rangle $$
⟨
⋁
,
∧
,
→
,
0
⟩
-structure of frames is also obtained.
Funder
Università degli Studi di Cagliari
Publisher
Springer Science and Business Media LLC
Subject
History and Philosophy of Science,Logic
Reference31 articles.
1. Abad, M., J. P. Diaz Varela, L. A. Rueda, and A. M. Suardíaz, Varieties of three-valued Heyting algebras with a quantifier, Studia Logica 65(2):181–198, 2000.
2. Balbes, R., and Ph. Dwinger, Distributive Lattices, University of Missouri Press, Columbia, 1974.
3. Banaschewski, B., Frames and compactifications, in Extensions Theory of Topological Structures and its Applications, Deutscher Verlag der Wissenschaften, 1969.
4. Banaschewski, B., and C. Gilmour, Stone–Cech compactification and dimension theory for regular $$\sigma $$-frames, Journal of the London Mathematical Society 2(127, 39, part 1):1–8, 1989.
5. Banaschewski, B., On the injectivity of Boolean algebras, Commentationes Mathematicae Universitatis Carolinae 34:501–511, 1993.