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TYCHONOFF HED-SPACES AND ZEMANIAN EXTENSIONS OF S4.3

Published online by Cambridge University Press:  14 January 2018

GURAM BEZHANISHVILI ,
NICK BEZHANISHVILI ,
JOEL LUCERO-BRYAN  and
JAN VAN MILL
GURAM BEZHANISHVILI*
Affiliation:
Department of Mathematical Sciences, New Mexico State University
NICK BEZHANISHVILI*
Affiliation:
Institute for Logic, Language and Computation, University of Amsterdam
JOEL LUCERO-BRYAN*
Affiliation:
Department of Applied Mathematics and Sciences, Khalifa University of Science and Technology
JAN VAN MILL*
Affiliation:
Korteweg-de Vries Institute for Mathematics, University of Amsterdam
*
*DEPARTMENT OF MATHEMATICAL SCIENCES NEW MEXICO STATE UNIVERSITY LAS CRUCES, NM 88003, USA E-mail: guram@math.nmsu.edu
†INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION UNIVERSITY OF AMSTERDAM 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: N.Bezhanishvili@uva.nl
‡DEPARTMENT OF APPLIED MATHEMATICS AND SCIENCES KHALIFA UNIVERSITY OF SCIENCE AND TECHNOLOGY ABU DHABI, UAE E-mail: joel.lucero-bryan@kustar.ac.ae
§KORTEWEG-DE VRIES INSTITUTE FOR MATHEMATICS UNIVERSITY OF AMSTERDAM 1098 XG AMSTERDAM, THE NETHERLANDS E-mail: j.vanMill@uva.nl
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Abstract

We introduce the concept of a Zemanian logic above S4.3 and prove that an extension of S4.3 is the logic of a Tychonoff HED-space iff it is Zemanian.

Keywords

03B4554G05modal logictopological completenesshereditarily extremally disconnected space
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 1 , March 2018 , pp. 115 - 132
Copyright
Copyright © Association for Symbolic Logic 2018 

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References

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