S4.3 and hereditarily extremally disconnected spaces:

Guram Bezhanishvili; Nick Bezhanishvili; Joel Lucero-Bryan; Jan van Mill

doi:10.1515/gmj-2015-0041

Published by De Gruyter October 20, 2015

S4.3 and hereditarily extremally disconnected spaces

Guram Bezhanishvili , Nick Bezhanishvili , Joel Lucero-Bryan and Jan van Mill

From the journal Georgian Mathematical Journal

https://doi.org/10.1515/gmj-2015-0041

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Abstract

The modal logic S4.3 defines the class of hereditarily extremally disconnected spaces (HED-spaces). We construct a countable HED-subspace X of the Gleason cover of the real closed unit interval [0,1] such that S4.3 is the logic of X.

Keywords: Modal logic; topological semantics; topological completeness; hereditarily extremally disconnected space

MSC: 03B45; 54G05

Received: 2015-7-6

Accepted: 2015-8-27

Published Online: 2015-10-20

Published in Print: 2015-12-1

S4.3 and hereditarily extremally disconnected spaces

Abstract

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