On some connections between Boolean algebras and Heyting algebras

Dimitrii E. Pal'chunov; Alain Touraille

Annales scientifiques de l'Université de Clermont. Mathématiques (1992)

  • Volume: 98, Issue: 28, page 5-16
  • ISSN: 0249-7042

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Pal'chunov, Dimitrii E., and Touraille, Alain. "On some connections between Boolean algebras and Heyting algebras." Annales scientifiques de l'Université de Clermont. Mathématiques 98.28 (1992): 5-16. <http://eudml.org/doc/80598>.

@article{Palchunov1992,
author = {Pal'chunov, Dimitrii E., Touraille, Alain},
journal = {Annales scientifiques de l'Université de Clermont. Mathématiques},
keywords = {Heyting algebras; Boolean algebras; first-order definable; finite axiomatizability},
language = {eng},
number = {28},
pages = {5-16},
publisher = {UER de Sciences exactes et naturelles de l'Université de Clermont},
title = {On some connections between Boolean algebras and Heyting algebras},
url = {http://eudml.org/doc/80598},
volume = {98},
year = {1992},
}

TY - JOUR
AU - Pal'chunov, Dimitrii E.
AU - Touraille, Alain
TI - On some connections between Boolean algebras and Heyting algebras
JO - Annales scientifiques de l'Université de Clermont. Mathématiques
PY - 1992
PB - UER de Sciences exactes et naturelles de l'Université de Clermont
VL - 98
IS - 28
SP - 5
EP - 16
LA - eng
KW - Heyting algebras; Boolean algebras; first-order definable; finite axiomatizability
UR - http://eudml.org/doc/80598
ER -

References

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  2. [2] A. Macintyre and J.G. Rosenstein, X0-categoricity for rings without nilpotent elements and for Boolean structures, Journal of Algebra, vol. 43 (1976) pp. 129-154. Zbl0346.02031MR429545
  3. [3] B. Molzan, On the theory of Boolean algebras with Ramsey quantifiers, Proceedings of the third Easter conference on model theory (Gros-Köris, 1985), Seminarberichte No 70, Sektion Mathematik, Humboldt-Universität, Berlin, 1985, pp. 186-192. Zbl0591.03017MR824287
  4. [4] D.E. Pal'chunov, On undecidability of theories of boolean algebras with distinguished ideals, Algebra and Logic, vol. 25 (1986), n°3, pp. 326-346. Zbl0628.03004MR903121
  5. [5] D.E. Pal'chunov, On prime and countably saturated Boolean algebras wilh distinguished ideals, Proceedings of the 8th Soviet Union Mathematical Logic Conference, Moskow, 1986, p. 147. 
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  7. [7] D.E. Pal'chunov, On Heyting algebras with finite number of dense elements, Computable invariants in the algebraic system theory, Novosibirsk, 1987, pp. 35-45. Zbl0709.06006MR979570
  8. [8] D.E. Pal'chunov, Finitely axiomatizable Boolean algebras with distinguished ideals, Algebra and Logic, vol. 26 (1987), n° 4, pp. 435-455. Zbl0647.03026MR963096
  9. [9] D.E. Pal'chunov, On the prime models of the theory of Boolean algebras with distinguished ideals, Proceedings of the Summer School and Conference "Kleene-90 ", Sofia, 1990, p. 59. 
  10. [10] D.E. Pal'chunov, Unlocal Boolean algebras with distinguished ideals, Proceedings of the Soviet and France Colloquium on Model Theory, Karaganda, 1990, pp. 35-36. 
  11. [11] D.E. Pal'chunov, Direct Summands of boolean algebras with distinguished ideals, Proceedings ofthe Logic Colloquxum' 90, Helsinki,1990, p. 60. 
  12. [12] D.E. Pal'chunov, Prime and countably saturated Boolean algebras, Proceedings of the Institute of Mathematics, Nauka, Novosibirsk, to appear. 
  13. [13] M.O. Rabin, Decidability of second-order theories and automata on infinite trees, Transactions of the American Mathematical Society, vol. 141 (1969), pp.1- 35. Zbl0221.02031MR246760
  14. [14] H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, Polska Akademia Nauk Monographi Mathematyczne 41, Warsawa, 1963. Zbl0122.24311MR163850
  15. [15] A. Touraille, Elimination des quantificateurs dans la théorie élémentaire des algèbres de Boole munies d'une famille d'idéaux distingués, Comptes-Rendus des Séances de l'Académie des Sciences, Série I: Mathématique, vol. 300 (1985), pp. 125-128. Zbl0584.03020MR779692
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