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Equality in

Published online by Cambridge University Press:  12 March 2014

Jonathan P. Seldin
Jonathan P. Seldin*
Affiliation:
Southern Illinois University, Carbondale, Illinois 62901
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Extract

In [CLg. II, §15B6], the problem of representing equality in the system by means of an ob Q is discussed; it is shown there that if Q is taken to be a canonical atom of degree 2 and if the axiom scheme

is postulated, then it follows by Rule Eq that

and, if no other properties are postulated for Q, then the converse of (1), Q-consistency, also holds. However, it is also desirable to have, in addition, the property

at least for some obs Z, and the statement is made in [CLg. II, §15B6] that no known way of incorporating this principle existed (at the time this statement was written) in such a way that there was a proof of Q-consistency. In this paper it is shown that if Z is restricted to be a basic canob of degree 1, i.e., if Z is restricted to be a predicate of one argument, then a system in which (2) is postulated can be proved Q-consistent.

The notations and conventions of [CLg. II] especially §15B, will be used throughout the paper.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 4 , December 1973 , pp. 571 - 575
Copyright
Copyright © Association for Symbolic Logic 1973

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References

REFERENCE

[CLg. II] Curry, H. B., Hindley, J. R. and Seldin, J. P., Combinatory logic. Vol. 2, North-Holland, Amsterdam, 1972.Google Scholar