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Generic Embeddings

Published online by Cambridge University Press:  12 March 2014

Jacob Manuel Plotkin
Jacob Manuel Plotkin*
Affiliation:
Cornell University
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Extract

Since Cohen [1] showed the independence of the axiom of choice from the other axioms of ZF, a number of people have used his forcing technique to show how badly choice can fail while certain vestiges of it remain. Many of these arguments involve the introduction of a generic sequence or generic set of generic sets of ordinals into a countable standard model of ZF + V = L. The desired results then follow by the use of clever permutation and forcing arguments. (See Cohen [2, pp. 136–142].)

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 34 , Issue 3 , 17 November 1969 , pp. 388 - 394
Copyright
Copyright © Association for Symbolic Logic 1969

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References

[1]Cohen, P. J., Independence of the axiom of choice, Stanford University, Stanford, Calif., 1963.Google Scholar
[2]Cohen, P. J., Set theory and the continuum hypothesis, Benjamin, New York, 1966.Google Scholar
[3] A. Lévy, Definability in axiomatic set theory, I. Logic, methodology and the philosophy of science, Proceedings of the 1964 International Congress, North-Holland, Amsterdam, 1965, pp. 127–151.Google Scholar
[4]Morley, M. and Vaught, R., Homogeneous universal models, Mathematica scandanavica, vol. 11 (1962), pp. 37–57.CrossRefGoogle Scholar
[5]Vaught, R., Denumerable models of complete theories, Proceedings of the symposium on foundations of mathematics, infinitistic methods, Warsaw, Pergamon Press, Krakow, 1961, pp. 303–321.Google Scholar