Profinite Heyting Algebras

@article{Bezhanishvili2008ProfiniteHA,
  title={Profinite Heyting Algebras},
  author={Guram Bezhanishvili and Nick Bezhanishvili},
  journal={Order},
  year={2008},
  volume={25},
  pages={211-227}
}
For a Heyting algebra A, we show that the following conditions are equivalent: (i) A is profinite; (ii) A is finitely approximable, complete, and completely joinprime generated; (iii) A is isomorphic to the Heyting algebra Up(X) of upsets of an image-finite poset X. We also show that A is isomorphic to its profinite completion iff A is finitely approximable, complete, and the kernel of every finite homomorphic image of A is a principal filter of A. 
Highly Cited
This paper has 24 citations. REVIEW CITATIONS

From This Paper

Figures and tables from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 12 references

Lattices of intermediate and cylindric modal logics

N. Bezhanishvili
Ph.D. thesis, University of Amsterdam (2006) Order • 2008

Heyting Algebras I

L. L. Esakia
Duality Theory (Russian). Metsniereba, Tbilisi • 1985

Stone Spaces

P. T. Johnstone
Cambridge University Press, Cambridge • 1982

On the theory of modal and superintuitionistic systems

L. L. Esakia
Logical Inference (Moscow, 1974), pp. 147–172. Nauka, Moscow • 1979

Topological Kripke models

L. L. Esakia
Sov. Math. Dokl. 15, 147–151 • 1974
View 2 Excerpts

Algebraic Systems

A. I. Malcev
Springer, New York • 1973