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An extension of basic logic1

Published online by Cambridge University Press:  12 March 2014

Frederic B. Fitch
Frederic B. Fitch*
Affiliation:
Yale University
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Extract

A logical calculus Κ was defined in a previous paper and then shown in a subsequent paper to contain within itself a representation of every constructively definable subclass of expressions of a certain infinite class U of expressions, where Κ itself is one such subclass. (The former paper will be referred to as BL and the latter paper as RC.) The calculus Κ was called a “basic calculus” and its theorems were thought of as expressing the asserted propositions of a “basic logic,” that is, of a logic within which is definable every constructively definable system of logic and indeed every constructively definable class or relation. The notion of constructive definability was essentially equated with the notion of recursive enumerability.

Type
Articles
Information
The Journal of Symbolic Logic , Volume 13 , Issue 2 , June 1948 , pp. 95 - 106
Copyright
Copyright © Association for Symbolic Logic 1948

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Footnotes

1

This paper is largely an outcome of work done by the author while holding a John Simon Guggenheim Memorial Foundation Fellowship during the academic year 1945–46. It bears a very close relationship to the author's paper, A system of relations and classes, read before the ninth meeting of the Association for Symbolic Logic and summarized in this Journal, vol. 12 (1947), pp. 30–31. In the first line of the summary the word ‘consistent’ was supposed to have been deleted since the consistency of that system has not been proved.

References

4 A minimum calculus for logic, ibid., vol. 9 (1944), pp. 89–94.

5 This Journal, vol. 1 (1936), pp. 87–91.