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Algebraic semantics for the ( ↔ , ¬ ) ‐fragment of IPC and its properties
Author(s) -
Słomczyńska Katarzyna
Publication year - 2017
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201600046
Subject(s) - fragment (logic) , mathematics , algebraic semantics , variety (cybernetics) , algebraic number , propositional calculus , zero (linguistics) , construct (python library) , semantics (computer science) , pure mathematics , finitely generated abelian group , algebra over a field , discrete mathematics , computer science , algorithm , programming language , linguistics , mathematical analysis , statistics , philosophy
We study the variety of equivalential algebras with zero and its subquasivariety that gives the equivalent algebraic semantics for the ( ↔ , ¬ ) ‐fragment of intuitionistic propositional logic. We prove that this fragment is hereditarily structurally complete. Moreover, we effectively construct the finitely generated free equivalential algebras with zero.