On the problem of R. E. Tax

• Autorzy: Wojtylak P. , Wroński A.
• Języki publikacji: EN

Abstrakty

EN

We prove that the purely equivalential fragment of intuitionic logic is not axiomatizable by a finite number of axiom schemata and the modus ponens rule for equivalence as the only rule of inference.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2001
• Tom: No. 35
• Strony: 87--101
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Wojtylak P.

• Uniwersytet Śląski Instytut Matematyki ul. Bankowa 14 40-007 Katowice

autor

Wroński A.

• Department of Logic Jagiellonian University Grodzka 52 Kraków 31-044, Poland

Bibliografia

• [1] J. R. Büchi and T. M. Owens, Skolem rings and their varieties, in The Collected Works of J. Richard Büchi, S. MacLane and D. Siefkes, eds., Springer-Verlag, Berlin, 1990, 161–221.
• [2] L. Henkin, J. D. Monk, and Tarski, Cylindric Algebras, I, North-Holland, Amsterdam, 1971. Studies in Logic and Foundations of Mathematics.
• [3] K. Idziak, Quasivarieties of equivalential algebras, Reports on Mathematical Logic, 29 (1995), 81–85.
• [4] K. Idziak, Equivalential logics with constants, PhD thesis, Jagiellonian University, 1998.
• [5] P. M. Idziak, K. Słomczyńska, and A. Wro´nski, Equivalential algebras: A study of fregean varieties. Manuscript, 1996.
• [6] P. M. Idziak and A. Wro´nski, Definability of principal congruences in equivalential algebras, Colloquium Mathematicum, 74 (1997), 225–238.
• [7] B. Jónsson and A. Tarski, On two properties of free algebras, Math. Scand., 9 (1961), 95–101.
• [8] J. K. Kabziński and A. Wro´nski, On equivalential algebras, in Proceedings of the 1975 International Symposium on Multiple-Valued Logic, Long Beach, Calif., 1975, IEEE Comput. Soc., 419–428. (Indiana University, Bloomington, Ind., May 13–16, 1975).
• [9] K. Słomczyńska, Equivalential algebras, PhD thesis, Jagiellonian University, 1994.
• [10] K. Słomczyńska, Equivalential algebras, part i: Representation theorem, Algebra Universalis, 35 (1996), 524–547.
• [11] R. E. Tax,On the intuitionistic equivalential fragment, Notre Dame Journal of Formal Logic, 14 (1973), 448–456.