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A Finite Hilbert‐Style Axiomatization of the Implication‐Less Fragment of the Intuitionistic Propositional Calculus
Author(s) -
Rebagliato Jordi,
Verdú Ventura
Publication year - 1994
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.19940400109
Subject(s) - mathematics , fragment (logic) , closure (psychology) , propositional calculus , calculus (dental) , algebra over a field , propositional variable , pure mathematics , discrete mathematics , intermediate logic , algorithm , computer science , medicine , dentistry , programming language , economics , market economy , description logic
In this paper we obtain a finite Hilbert‐style axiomatization of the implicationless fragment of the intuitionistic propositional calculus. As a consequence we obtain finite axiomatizations of all structural closure operators on the algebra of {–}‐formulas containing this fragment. Mathematics Subject Classification: 03B20, 03B22, 06D15.