Grzegorczyk Algebras Revisited

Stronkowski, Michał M.

dc.contributor.author	Stronkowski, Michał M.
dc.date.accessioned	2019-01-14T14:54:40Z
dc.date.available	2019-01-14T14:54:40Z
dc.date.issued	2018
dc.identifier.issn	0138-0680
dc.identifier.uri	http://hdl.handle.net/11089/26417
dc.description.abstract	We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.	en_GB
dc.description.sponsorship	The work was supported by the Polish National Science Centre grant no. DEC- 2011/01/D/ST1/06136.	en_GB
dc.language.iso	en	en_GB
dc.publisher	Wydawnictwo Uniwersytetu Łódzkiego	en_GB
dc.relation.ispartofseries	Bulletin of the Section of Logic;2
dc.rights	This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.	en_GB
dc.rights.uri	http://creativecommons.org/licenses/by-nc-nd/4.0	en_GB
dc.subject	Grzegorczyk algebras	en_GB
dc.subject	free Boolean extensions of Heyting algebras	en_GB
dc.subject	stable homomorphisms	en_GB
dc.title	Grzegorczyk Algebras Revisited	en_GB
dc.type	Article	en_GB
dc.page.number	[129]-139
dc.contributor.authorAffiliation	Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland
dc.identifier.eissn	2449-836X
dc.references	G. Bezhanishvili and N. Bezhanishvili, An algebraic approach to canonical formulas: modal case, Studia Logica 99 (2011), pp. 93–125.	en_GB
dc.references	G. Bezhanishvili, N. Bezhanishvili and R. Iemhoff, Stable canonical rules, Journal of Symbolic Logic 81 (2016), pp. 284–315.	en_GB
dc.references	W. J. Blok, Varieties of interior algebras, PhD thesis, University of Amsterdam (1976), URL=http://www.illc.uva.nl/Research/Dissertations/HDS-01-Wim_Blok.text.pdf.	en_GB
dc.references	W. J. Blok and Ph. Dwinger, Equational classes of closure algebras. I, Indagationes Mathematicae 37 (1975), pp. 189–198.	en_GB
dc.references	A. Chagrov and M. Zakharyaschev, Modal logic, Oxford University Press, New York, 1997.	en_GB
dc.references	A. Chagrov and M. Zakharyashchev, Modal companions of intermediate propositional logics, Studia Logica 51 (1992), pp. 49–82.	en_GB
dc.references	L. L. Esakia, On the theory of modal and superintuitionistic systems, [in:] V. A. Smirnov (ed.), Logical inference, Nauka, Moscow (1979), pp. 147–172 (in Russian).	en_GB
dc.references	L. L. Esakia, On the variety of Grzegorczyk algebras, [in:] Studies in nonclassical logics and set theory, Nauka, Moscow (1979), pp. 257–287 (in Russian).	en_GB
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dc.references	S. Givant and P. Halmos, Introduction to Boolean algebras, Springer, New York, 2009.	en_GB
dc.references	A. Grzegorczyk, Some relational systems and the associated topological spaces, Fundamenta Mathematicae 60 (1967), pp. 223–231.	en_GB
dc.references	D. C. Makinson, On the number of ultrafilters of an infinite boolean algebra, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (1969), pp. 121–122.	en_GB
dc.references	L. L. Maksimova and V. V. Rybakov, The lattice of normal modal logics, Algebra and Logic 13 (1974), pp. 105–122.	en_GB
dc.references	J. C. C. McKinsey and A. Tarski, On closed elements in closure algebras, Annals of Mathematics 47 (1946), pp. 122–162.	en_GB
dc.references	A. Y. Muravitsky, The embedding theorem: its further developments and consequences. Part I, Notre Dame Journal of Formal Logic 47 (2006),pp. 525–540.	en_GB
dc.references	M. M. Stronkowski, Free Boolean extensions of Heyting algebras, Advances in Modal Logic, Budapest, 2016, pp. 122–126 (Extended abstract).	en_GB
dc.references	M. M. Stronkowski, On the Blok-Esakia theorem for universal classes, arXiv:1810.09286.	en_GB
dc.references	F. Wolter and M. Zakharyaschev, On the Blok-Esakia theorem, [in:] G. Bezhanishvili (ed.), Leo Esakia on Duality in Modal and Intuitionistic Logics, Springer Netherlands, Dordrecht (2014), pp. 99–118.	en_GB
dc.references	M. Zakharyaschev, Canonical formulas for K4. Part I. Basic results Journal of Symbolic Logic 57 (1992), pp. 1377–1402.	en_GB
dc.contributor.authorEmail	m.stronkowski@mini.pw.edu.pl
dc.identifier.doi	10.18778/0138-0680.47.2.05
dc.relation.volume	47	en_GB
dc.subject.jel	03G25
dc.subject.jel	06E25
dc.subject.jel	06D20
dc.subject.jel	03B45

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