Abstract
Let µ1= Cpq, with µm+1 = Cpµm. Then Meyer has shown (70a, p. 387) that for i < j, Cµiµj is not provable in Church’s weak implicational calculus R I . It follows, of course, that R I has no finite characteristic matrix; and Pahi has suggested in 72 ways of extending this latter result to a wide class of subsystems of R I . In fact, however, modifications of the method of (Ulrich 71) permit complete extension.
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© 1989 Kluwer Academic Publishers
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Ulrich, D. (1989). Nonexistence of Finite Characteristic Matrices for Subsystems of R1. In: Norman, J., Sylvan, R. (eds) Directions in Relevant Logic. Reason and Argument, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1005-8_12
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DOI: https://doi.org/10.1007/978-94-009-1005-8_12
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6942-7
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