ON THE GALOIS CONNECTION FOR CLOSED CLASSES OF INFINITARY FUNCTIONS

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Resumo

In this paper, Galois theory is developed for closed sets of functions of any ordinal arity. The classical theorem on Galois-closed classes of functions and sets of predicates on finite sets is transferred to the general case.

Sobre autores

N. Polyakov

HSE University

Email: produktov@hse.ru
Moscow, Russia

M. Shamolin

Moscow State University named after M. V. Lomonosov

Email: shamolin@imec.msu.ru
Corresponding member of the RAS Moscow, Russia

Bibliografia

  1. Geiger D. Closed systems of functions and predicates // Pacific journal of mathematics. 1968. V. 27. № 1. P. 95–100.
  2. Bodnarchuk V.G., Kaluzhnin L.A., Kotov V.N. et al. Galois theory for Post algebras. I–II // Cybern Syst Anal. 1969. V. 5. P. 243–252 and 531–539.
  3. Lau D. Function Algebras on Finite Sets. A Basic Course on Many-Valued Logic and Clone Theory. Berlin–Heidelberg: Springer-Verlag, 2006.
  4. Pöschel R., Kaluznin L.A. Funktionenund Relationenalgebren. Berlin: WEB Deutscher Verlag der Wissenschaften, 1979.
  5. Parvatov N.G. Galois correspondence for closed classes of discrete functions // Prikl. Diskr. Mat. 2010. V. 2. № 8. P. 10–15 (Russian).
  6. Polyakov N.L. Functional Galois connections and a classification of symmetric conservative clones with a finite carrier / arXiv:1810.02945. 2018.
  7. Zhuk D.N. The predicate method to construct the Post lattice // Discrete Math. Appl. 2011. V. 21. № 3. P. 329–344.
  8. Поляков Н.Л., Шамолин М.В. Об одном обобщении теоремы Эрроу // Доклады РАН. 2014. T. 456. № 2. C. 143–145.
  9. Slominski J. Theory of models with infinitary operations and relations // Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 1958. V. 6. P. 449–456.
  10. Slominski J. The theory of abstract algebras with infinitary operations // Rozprawy Mat. 18. 1959.
  11. Hansoul G.E. The Frattini subalgebra of an infinitary algebra. Bull. Soc. Roy. Sci. Liège 49 (1980), 423–424.
  12. Lipparini P. Non-generators in extensions of infinitary algebras // Reports on Math. Logic. 2022. V. 57. P. 31–43.
  13. Diener K.H. An application of infinitary universal algebra to set theory // Algebra Universalis. 1994. V. 32. P. 297–306.
  14. Bucciarelli A. and Salibra A. An algebraic theory of clones // Algebra Universalis. 2022. V. 83. № 2. P. 1–30.
  15. Bucciarelli A., Curienet P.-L. et al. Birkhoff-style Theorems Through Infinitary Clone Algebras / arXiv:2411.16386. 2024.
  16. Polyakov N.L. Closed classes of infinitary functions and their applications in ultrafilter theory // Algebra and Model Theory. 2023. V. 14. P. 102–112 (Russian).
  17. Grätzer G. General Lattice Theory (second edition). Birkhäuser Basel, Birkhäuser Verlag, 2003.
  18. Jeh T. Set Theory. Springer Monographs in Mathematics (third millennium ed.). Berlin, New York, 2003.
  19. Comfort W.W., Negrepontis S. The theory of ultrafilters. Berlin: Springer, 1974.
  20. Kartashova A.V. On lattices of topologies of unary algebras // J. of Math. Sci. 2003. V. 114. № 2. P. 1086–1118.
  21. Juhász I. Cardinal functions in topology // Mathematical Centre Tracts No. 34. Mathematisch Centrum Amsterdam, 1971.

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