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2014 | 23 | 4 | 481–497
Article title

Three-element non-finitely axiomatizable matrices and term-equivalence

Title variants
Languages of publication
EN
Abstracts
EN
It was shown in [5] that all two-element matrices are finitely based independently of their classification by term equivalence (the Post classification). In particular, each 2-valued matrix is finitely axiomatizable. We show below that for certain two not finitely axiomatizable 3-valued matrices this property is also preserved under term equivalence. The general problem, whether finite axiomatizability of a finite matrix is preserved under term-equivalence, is still open, as well as the related problem as to whether the consequence operation of a finite matrix is finitely based.
Year
Volume
23
Issue
4
Pages
481–497
Physical description
Dates
published
2014-12-01
online
2014-04-30
Contributors
  • Cracow University of Technology, Department of Mathematics, ul. Warszawska 24, Kraków, Poland, kpalasinska@gmail.com
References
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  • Blok, W., and D. Pigozzi, Algebraizable Logics, Memoirs of the AMS, 396, Providence, 1989. DOI: 10.1090/memo/0396
  • Blok, W., D. Pigozzi, “Algebraic semantics for universal Horn logic without equality”, in: Universal Algebra abd Quasigroup Theory, A. Romanowska and J.D.H.Smith (eds.), Heldermann Verlag, Berlin, 1992.
  • Dziobiak, W., “A finite matrix whose set of tautologies is not finitely axiomatizable”, Reports on Mathematical Logic, 25 (1991): 113–117.
  • Herrmann, B., and W. Rautenberg, “Finite replacement and Finite Hilbert-style axiomatizability”, Mathematical Logic Quarterly, 38 (1992): 327–344.
  • Pałasińska, K., “Three-element nonfinitely axiomatizable matrices”, Studia Logica, 53 (1994): 361–372.
  • Pałasińska, K., “No matrix term-equivalent to Wroński’s 3-element matrix is finitely based”, Studia Logica, 77 (2004): 413–423.
  • Rautenberg, W., “Two-element matrices”, Studia Logica, 40 (1981): 315–353.
  • Wojtylak, P., “Strongly finite logics: Finite axiomatizability and the problem of supremum”, Bulletin of the Section of Logic, 8 (1979): 99–111.
  • Wojtylak, P., “An example of a finite though finitely non-axiomatizable matrix”, Reports on Mathematical Logic, 17 (1984): 39–46.
  • Wroński, A., “A Three-element matrix whose consequence operation is not finitely based”, Bulletin of the Section of Logic, 8 (1979): 68–71.
Document Type
Publication order reference
Identifiers
YADDA identifier
bwmeta1.element.desklight-30ee7d4f-7f68-4c8b-a121-c595d76a51c1
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