Proof of the independence of the primitive symbols of Heyting's calculus of propositions
- 1 December 1939
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 4 (4) , 155-158
- https://doi.org/10.2307/2268715
Abstract
In this paper I shall show that no one of the four primitive symbols of Heyting's calculus of propositions is definable in terms of the other three. So as to make the paper self-contained, I begin by stating the rules and primitive sentences given by Heyting.The primitive symbols of the calculus are “⅂”, “∨”, “∧”, and “⊃”, which may be read, respectively, as “not,” “either…or,” “and,” and “if…then.” The symbol “⊃⊂”, which may be read “if and only if,” is defined in terms of these as follows: The rule of substitution is assumed, and the rule that S2 follows from S1 and S1⊃S2; in addition it is assumed that S1∧S2 follows from S1 and S2. The primitive sentences are as follows:Keywords
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