Grzegorczyk Algebras Revisited

Michał M. Stronkowski

Bulletin of the Section of Logic (2018)

  • Volume: 47, Issue: 2
  • ISSN: 0138-0680

Abstract

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

How to cite

top

Michał M. Stronkowski. "Grzegorczyk Algebras Revisited." Bulletin of the Section of Logic 47.2 (2018): null. <http://eudml.org/doc/295539>.

@article{MichałM2018,
abstract = {We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.},
author = {Michał M. Stronkowski},
journal = {Bulletin of the Section of Logic},
keywords = {Grzegorczyk algebras; free Boolean extensions of Heyting algebras; stable homomorphisms},
language = {eng},
number = {2},
pages = {null},
title = {Grzegorczyk Algebras Revisited},
url = {http://eudml.org/doc/295539},
volume = {47},
year = {2018},
}

TY - JOUR
AU - Michał M. Stronkowski
TI - Grzegorczyk Algebras Revisited
JO - Bulletin of the Section of Logic
PY - 2018
VL - 47
IS - 2
SP - null
AB - We provide simple algebraic proofs of two important facts, due to Zakharyaschev and Esakia, about Grzegorczyk algebras.
LA - eng
KW - Grzegorczyk algebras; free Boolean extensions of Heyting algebras; stable homomorphisms
UR - http://eudml.org/doc/295539
ER -

References

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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.