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Projective prewellorderings vs projective wellfounded relations

  • Xianghui Shi (a1)

Abstract

We show that it is relatively consistent with ZFC that there is aprojective wellfounded relation with rank higher than all projective prewellorderings.

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[1]Erdős, Paul, Hajnal, Andras, and Rado, Richard, Partition relations for cardinal numbers. Acta Mathematica Academias Scientiarum Hungaricae, vol. 16 (1965), pp. 93196.
[2]Harrington, L. A., Long projective wellorderings, Annals of Mathematical Logic, vol. 12 (1977), pp. 124.
[3]Jech, Thomas, Set Theory, 3rd (millenium, revised and expanded) ed., Springer, 2003.
[4]Kechris, Alexander S.. On projective ordinals, this Journal, vol. 39 (1974), no. 2, pp. 269282.
[5]Kechris, Alexander S., Solovay, Robert M., and Steel, John R., The Axiom of Determinacy and the prewellordering property, Cabal Seminar '77–'79 (Proceedings of the Caltech-UCLA Logic Seminar, 1977-1979), Springer, 1981, pp. 101125.
[6]Kunen, Kenneth, Set Theory: An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland, 1980.
[7]Moschovakis, Yiannis N., Determinacy and prewellorderings of the continuum, Mathematical Logic and Foundations of Set Theory (Bar-Hillel, Y., editor), North-Holland, 1970, pp. 2462.
[8]Moschovakis, Yiannis N., Descriptive Set Theory, North-Holland Publishing Co., 1980.
[9]Shi, Xianghui, Prewellorderings vs wellfounded relations, Ph.D. thesis. University of California at Berkeley, 2006.
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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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