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Licensed Unlicensed Requires Authentication Published by De Gruyter October 20, 2015

S4.3 and hereditarily extremally disconnected spaces

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

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.

MSC: 03B45; 54G05
Received: 2015-7-6
Accepted: 2015-8-27
Published Online: 2015-10-20
Published in Print: 2015-12-1

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