Description

• Title:
  On Pre-Hilbert and Positive Implicative Pre-Hilbert Algebras
• Creator:
  Walendziak, Andrzej
• Contributor:
  University of Siedlce, Faculty of Exact and Natural Sciences, Institute of Mathematics;
  walent@interia.pl
• Description:
  In the paper, pre-Hilbert algebras are defined as a generalization of Hilbert algebras (namely, a Hilbert algebra is just a pre-Hilbert algebra satisfying the property of antisymmetry). Pre-Hilbert algebras have been inspired by Henkin’s Positive Implicative Logic. Their properties and characterizations are investigated. Some important results and examples are given. Moreover, positive implicative pre-Hilbert algebras are introduced and studied, their connections with some algebras of logic are presented. The hierarchies existing between the classes of algebras considered here are shown.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2024.09.30;
  2024.05.20
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic;3;
  53
• Subject:
  Hilbert algebra;
  pre-Hilbert algebra;
  BCK-algebra;
  BCC-algebra;
  BE-algebra;
  positive implicativity
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/53272 ;
  2449-836X;
  10.18778/0138-0680.2024.07
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image