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Some results on combinators in the system TRC

Published online by Cambridge University Press:  12 March 2014

Thomas Jech
Thomas Jech*
Affiliation:
Department of Mathematics, The Pennsylvania State University, 218 Mcallister Bldg., University Park, PA 16802, U.S.A., E-mail: [email protected]
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Abstract

We investigate the system TRC of untyped illative combinatory logic that is equiconsistent with New Foundations. We prove that various unstratified combinators do not exist in TRC.

Keywords

CombinatorsTRCNew Foundations
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1811 - 1819
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

[1]Curry, H. and Feys, R., Combinatory logic, North-Holland Publishing Company, Amsterdam, 1958.Google Scholar
[2]Hindley, J. R. and Seldin, J. P., Introduction to combinators and λ-calculus, Cambridge University Press, 1986.Google Scholar
[3]Holmes, M. R., Systems of combinatory logic related to Quine's ‘New Foundations’, Annals of Pure and Applied Logic, vol. 53 (1991), pp. 103–133.CrossRefGoogle Scholar
[4]Jech, T., OTTER experiments in a system of combinatory logic, Journal of Automated Reasoning, vol. 14 (1995), pp. 413–426.CrossRefGoogle Scholar
[5]McCune, W. W., OTTER 3.0, Argonne National Laboratory, 1994.CrossRefGoogle Scholar
[6]Quine, W. V., New foundations for mathematical logic, The American Mathematical Monthly, vol. 44 (1937), pp. 70–80.CrossRefGoogle Scholar
[7]Smullyan, R., To mock a mockingbird, A. Knopf, New York, 1985.Google Scholar