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    Beklemishev, Lev Bezhanishvili, Guram Mundici, Daniele and Venema, Yde 2012. Foreword. Studia Logica, Vol. 100, Issue. 1-2, p. 1.


    Lucero-Bryan, Joel 2011. The d-Logic of the Rational Numbers: A Fruitful Construction. Studia Logica, Vol. 97, Issue. 2, p. 265.


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THE MODAL LOGIC OF STONE SPACES: DIAMOND AS DERIVATIVE

  • GURAM BEZHANISHVILI (a1), LEO ESAKIA (a2) and DAVID GABELAIA (a2)
  • DOI: http://dx.doi.org/10.1017/S1755020309990335
  • Published online: 01 January 2010
Abstract

We show that if we interpret modal diamond as the derived set operator of a topological space, then the modal logic of Stone spaces is K4 and the modal logic of weakly scattered Stone spaces is K4G. As a corollary, we obtain that K4 is also the modal logic of compact Hausdorff spaces and K4G is the modal logic of weakly scattered compact Hausdorff spaces.

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Corresponding author
*DEPARTMENT OF MATHEMATICAL SCIENCES, NEW MEXICO STATE UNIVERSITY, LAS CRUCES, NM 88003. E-mail:gbezhani@nmsu.edu
DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:esakia@hotmail.com
DEPARTMENT OF MATHEMATICAL LOGIC, A. RAZMADZE MATHEMATICAL INSTITUTE, M. ALEKSIDZE STR. 1, TBILISI 0193, GEORGIA. E-mail:gabelaia@gmail.com
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Aiello , J. van Benthem , & G. Bezhanishvili (2003). Reasoning about space: The modal way. Journal of Logic and Computation, 13(6), 889920.

G. Bezhanishvili , L. Esakia , & D. Gabelaia (2005). Some results on modal axiomatization and definability for topological spaces. Studia Logica, 81(3), 325355.

G. Bezhanishvili , & P. J Morandi . (2010). Scattered and hereditarily irresolvable spaces in modal logic. Archive for Mathematical Logic.

L. Esakia (2004). Intuitionistic logic and modality via topology. Annals of Pure and Applied Logic, 127(1–3), 155170.

J. C. C. McKinsey , & A. Tarski (1944). The algebra of topology. Annals of Mathematics, 45, 141191.

J. Terasawa (1997). Metrizable compactification of ω is unique. Topology and its Applications, 76, 189191.

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The Review of Symbolic Logic
  • ISSN: 1755-0203
  • EISSN: 1755-0211
  • URL: /core/journals/review-of-symbolic-logic
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