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Transactions of the American Mathematical Society

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A new proof of the strong partition relation on $ \omega\sb 1$


Author: Steve Jackson
Journal: Trans. Amer. Math. Soc. 320 (1990), 737-745
MSC: Primary 03E60; Secondary 03E05, 03E15
DOI: https://doi.org/10.1090/S0002-9947-1990-0972702-8
MathSciNet review: 972702
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Abstract: Assuming the axiom of determinacy, we give a new proof of the strong partition relation on $ {\omega _1}$. The proof is direct and avoids appeal to complicated set-theoretic machinery.


References [Enhancements On Off] (What's this?)

  • [S] Jackson, A calculation of $ \delta _5^1$, Ph.D. thesis, UCLA, 1983.
  • 1. Steve Jackson, 𝐴𝐷 and the projective ordinals, Cabal Seminar 81–85, Lecture Notes in Math., vol. 1333, Springer, Berlin, 1988, pp. 117–220. MR 960900, https://doi.org/10.1007/BFb0084974
  • [A] S. Kechris, AD and infinite exponent partition relations, unpublished manuscript, Dec. 1977.
  • 2. Alexander S. Kechris, 𝐴𝐷 and projective ordinals, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 91–132. MR 526915
  • [A] S. Kechris and H. Woodin, Generic codes for uncountable ordinals, partition properties, and elementary embeddings, (unpublished manuscript).
  • [D] A. Martin, Unpublished notes on the strong partition relation on $ {\omega _1}$.
  • [Y] Yiannis N. Moschovakis, Descriptive set theory, Studies in Logic and the Foundations of Mathematics, vol. 100, North-Holland Publishing Co., Amsterdam-New York, 1980. MR 561709
  • [R] Robert M. Solovay, A Δ¹₃ coding of the subsets of 𝜔_{𝜔}, Cabal Seminar 76–77 (Proc. Caltech-UCLA Logic Sem., 1976–77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp. 133–150. MR 526916

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0972702-8
Keywords: Determinacy, strong partition relation
Article copyright: © Copyright 1990 American Mathematical Society

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