Publisher： Cambridge University Press
E-ISSN： 1943-5886|28|3|217-221
ISSN： 0022-4812
Source： The Journal of Symbolic Logic, Vol.28, Iss.3, 1963-09, pp. : 217-221
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Abstract
Recent interest in Łukasiewicz' Lℵ0, raises the question whether this axiomatic system can be simplified [2]. It is known that Łukasiewicz' fourth axiom CCCPQCQPCQP is dependent [4] p. 51. The axiomatic system resulting from deleting the fourth axiom from Lℵ0 will be shown to be “minimal” in the sense that the axioms and rules of inference are mutually independent; consequently, no further simplification of Lℵ0, is possible. By switching basic operators, however, simplified modifications of Lℵ0, can be constructed.
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