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  • Jacob Manuel Plotkin (a1)

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].)

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[1]Cohen, P. J., Independence of the axiom of choice, Stanford University, Stanford, Calif., 1963.
[2]Cohen, P. J., Set theory and the continuum hypothesis, Benjamin, New York, 1966.
[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. 127151.
[4]Morley, M. and Vaught, R., Homogeneous universal models, Mathematica scandanavica, vol. 11 (1962), pp. 3757.
[5]Vaught, R., Denumerable models of complete theories, Proceedings of the symposium on foundations of mathematics, infinitistic methods, Warsaw, Pergamon Press, Krakow, 1961, pp. 303321.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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