publication . Preprint . Article . 2017


Open Access English
  • Published: 27 Feb 2017
The variety of Brouwerian semilattices is amalgamable and locally finite, hence by well-known results due to W. H. Wheeler, it has a model completion (whose models are the existentially closed structures). In this paper, we supply for such a model completion a finite and rather simple axiomatization.
arXiv: Mathematics::Logic
free text keywords: Mathematics - Logic, 03G25 (Primary), 03C10, 06D20 (Secondary), Philosophy, Logic, Mathematics, Discrete mathematics, Algebra

[BJ13] Guram Bezhanishvili and Ramon Jansana. Esakia style duality for implicative semilattices. Applied Categorical Structures, 21(2):181-208, 2013.

[Cel03] Sergio Celani. Representation of hilbert algebras and implicative semilattices. Open Mathematics, 1(4):561-572, 2003.

[CK90] C. C. Chang and H. J. Kiesler. Model theory, volume 73 of Studies in Logic and the Foundations of Mathematics. North-Holland Publishing Co., third edition, 1990.

[DJ10] Luck Darni`ere and Markus Junker. Model completion of varieties of co-heyting algebras. arXiv:1001.1663, 2010.

[GvG01] Silvio Ghilardi and Samuel J. van Gool. A model-theoretic characterization of monadic second order logic on infinite words. Journal of Symbolic Logic, 201? to appear, preliminary version as CoRR abs/1503.08936.

[GvG16] Silvio Ghilardi and Sam van Gool. Monadic second order logic as the model companion of temporal logic. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, pages 417-426, 2016.

[GZ97] Silvio Ghilardi and Marek Zawadowski. Model completions and r-Heyting categories. Ann. Pure Appl. Logic, 88(1):27-46, 1997. [OpenAIRE]

[GZ02] Silvio Ghilardi and Marek Zawadowski. Sheaves, Games and Model Completions. Kluwer, 2002.

[Ko¨h81] K¨ohler. Brouwerian semilattices. Transactions of AMS, 268(1):103-126, 1981.

[McK68] C. G. McKay. The decidability of certain intermediate propositional logics. The Journal of Symbolic Logic, 33(2):258-264, 1968. [OpenAIRE]

[Nem65] W. C. Nemitz. Implicative semi-lattices. Trans. Amer. Math. Soc., 117:128-142, 1965.

[RdL89] Gerard R Renardel de Lavalette. Interpolation in fragments of intuitionistic propositional logic. The Journal of symbolic logic, 54(04):1419-1430, 1989.

[Sha93] V. Yu. Shavrukov. Subalgebras of diagonalizable algebras of theories containing arithmetic. Dissertationes Math. (Rozprawy Mat.), 323:82, 1993.

[VM86] L Vrancken-Mawet. Dualit´e pour les demi-lattis de brouwer. Bull. Soc. Roy. Sci. Li`ege, 55(2):346-352, 1986.

[Whe76] William H. Wheeler. Model-companions and definability in existentially complete structures. Israel J. Math., 25(3-4):305-330, 1976.

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publication . Preprint . Article . 2017