Grzegorczyk Algebras Revisited

• Autorzy: Michał M. Stronkowski
• Języki publikacji: EN

Abstrakty

EN

We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.

Słowa kluczowe

EN

Grzegorczyk algebras; free Boolean extensions of Heyting algebras; stable homomorphisms

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2018
• Tom: 47
• Numer: 2

Daty

wydano

2018-06-30

Twórcy

autor

Michał M. Stronkowski

• Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warsaw, Poland

Bibliografia

• [1] G. Bezhanishvili and N. Bezhanishvili, An algebraic approach to canonical formulas: modal case, Studia Logica 99 (2011), pp. 93–125.
• [2] G. Bezhanishvili, N. Bezhanishvili and R. Iemhoff, Stable canonical rules, Journal of Symbolic Logic 81 (2016), pp. 284–315.
• [3] 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
• [4] W. J. Blok and Ph. Dwinger, Equational classes of closure algebras. I, Indagationes Mathematicae 37 (1975), pp. 189–198.
• [5] A. Chagrov and M. Zakharyaschev, Modal logic, Oxford University Press, New York, 1997.
• [6] A. Chagrov and M. Zakharyashchev, Modal companions of intermediate propositional logics, Studia Logica 51 (1992), pp. 49–82.
• [7] 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).
• [8] 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).
• [9] S. Ghilardi, Continuity, freeness, and filtrations, Journal of Applied Non-Classical Logics 20 (2010), pp. 193–217.
• [10] S. Givant and P. Halmos, Introduction to Boolean algebras, Springer, New York, 2009.
• [11] A. Grzegorczyk, Some relational systems and the associated topological spaces, Fundamenta Mathematicae 60 (1967), pp. 223–231.
• [12] 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.
• [13] L. L. Maksimova and V. V. Rybakov, The lattice of normal modal logics, Algebra and Logic 13 (1974), pp. 105–122.
• [14] J. C. C. McKinsey and A. Tarski, On closed elements in closure algebras, Annals of Mathematics 47 (1946), pp. 122–162.
• [15] A. Y. Muravitsky, The embedding theorem: its further developments and consequences. Part I, Notre Dame Journal of Formal Logic 47 (2006),pp. 525–540.
• [16] M. M. Stronkowski, Free Boolean extensions of Heyting algebras, Advances in Modal Logic, Budapest, 2016, pp. 122–126 (Extended abstract).
• [17] M. M. Stronkowski, On the Blok-Esakia theorem for universal classes, arXiv:1810.09286.
• [18] 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.
• [19] M. Zakharyaschev, Canonical formulas for K4. Part I. Basic results Journal of Symbolic Logic 57 (1992), pp. 1377–1402.

Identyfikatory

DOI

10.18778/0138-0680.47.2.05