Hereditarily Structurally Complete Intermediate Logics: Citkin’s Theorem Via Duality

被引：0
作者：
Nick Bezhanishvili
Tommaso Moraschini
机构：
[1] University of Amsterdam,Institute for Logic, Language and Computation
[2] Universitat de Barcelona (UB),Departament de Filosofia, Facultat de Filosofia
来源：
Studia Logica | 2023年 / 111卷
关键词：
Intermediate logics; Structural completeness; Heyting algebras; Duality;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A deductive system is said to be structurally complete if its admissible rules are derivable. In addition, it is called hereditarily structurally complete if all its extensions are structurally complete. Citkin (1978) proved that an intermediate logic is hereditarily structurally complete if and only if the variety of Heyting algebras associated with it omits five finite algebras. Despite its importance in the theory of admissible rules, a direct proof of Citkin’s theorem is not widely accessible. In this paper we offer a self-contained proof of Citkin’s theorem, based on Esakia duality and the method of subframe formulas. As a corollary, we obtain a short proof of Citkin’s 2019 characterization of hereditarily structurally complete positive logics.
引用
收藏
页码：147 / 186
页数：39
相关论文
共 72 条
  • [1] Balbes R(1970)Injective and Projective Heyting Algebras Trans. Amer. Math. Soc. 148 549-559
  • [2] Horn A(1986)Finitely generated free Heyting algebras The Journal of Symbolic Logic 51 152-165
  • [3] Bellissima F(2008)Profinite Heyting algebras Order 25 211-227
  • [4] Bezhanishvili G(2008)The Kuznetsov-Gerciu and Rieger-Nishimura logics: the boundaries of the finite model property Logic and Logical Philosophy 17 73-110
  • [5] Bezhanishvili N(2007)An algebraic approach to subframe logics. Intuitionistic case Annals of Pure and Applied Logic 147 84-100
  • [6] Bezhanishvili G(2005)Locally finite varieties of Heyting algebras Algebra Universalis 54 465-473
  • [7] Bezhanishvili N(2017)Epimorphisms in varieties of residuated structures Journal of Algebra 492 185-211
  • [8] de Jongh D(2011)Finitely generated free heyting algebras via birkhoff duality and coalgebra Logical Methods in Computer Science 7 24-324
  • [9] Bezhanishvili G(2018)Stable formulas in intuitionistic logic Notre Dame Journal of Formal Logic 59 307-227
  • [10] Ghilardi S(1982)On the structure of varieties with equationally definable principal congruences I Algebra Universalis 15 195-288
12345678