Neighborhood models generalize the well-known relational models, or Kripke models, for
modal logic. Although the idea underlying neighborhood models is implicit in the seminal …

We develop the theory of Krull dimension for S4-algebras and Heyting algebras. This leads
to the concept of modal Krull dimension for topological spaces. We compare modal Krull …

It is a landmark theorem of McKinsey and Tarski that if we interpret modal diamond as
closure (and hence modal box as interior), then\mathsf S4 S 4 is the logic of any dense-in …

We provide partial solutions to two problems posed by Shehtman concerning the modal
logic of the\v {C} ech-Stone compactification of an ordinal space. We use the Continuum …

For a topological space X, let L (X) be the modal logic of X where□ is interpreted as interior
(and hence◇ as closure) in X. It was shown in [3] that the modal logics S4, S4. 1, S4. 2, S4 …

Within ZFC, we develop a general technique to topologize trees that provides a uniform
approach to topological completeness results in modal logic with respect to zero …

We prove strong completeness results for some modal logics with the universal modality,
with respect to their topological semantics over 0-dimensional dense-in-themselves metric …

We prove that the modal logic of a crowded locally compact generalized ordered space is.
This provides a version of the McKinsey–Tarski theorem for generalized ordered spaces. We …

TYCHONOFF HED-SPACES AND ZEMANIAN EXTENSIONS OF S4.3 Page 1 THE REVIEW
OF SYMBOLIC LOGIC Volume 11, Number 1, March 2018 TYCHONOFF HED-SPACES AND …

We consider products of modal logics in topological semantics and prove that the
topological product of S4. 1 and S4 is the fusion of logics S4. 1 and S4 plus one extra asiom …