Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A new proof of the strong partition relation on $\omega _ 1$
HTML articles powered by AMS MathViewer

by Steve Jackson PDF
Trans. Amer. Math. Soc. 320 (1990), 737-745 Request permission

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
    Jackson, A calculation of $\delta _5^1$, Ph.D. thesis, UCLA, 1983.
  • Steve Jackson, $\textrm {AD}$ and the projective ordinals, Cabal Seminar 81โ€“85, Lecture Notes in Math., vol. 1333, Springer, Berlin, 1988, pp.ย 117โ€“220. MR 960900, DOI 10.1007/BFb0084974
  • S. Kechris, AD and infinite exponent partition relations, unpublished manuscript, Dec. 1977.
  • Alexander S. Kechris, $\textrm {AD}$ and projective ordinals, Cabal Seminar 76โ€“77 (Proc. Caltech-UCLA Logic Sem., 1976โ€“77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp.ย 91โ€“132. MR 526915
  • S. Kechris and H. Woodin, Generic codes for uncountable ordinals, partition properties, and elementary embeddings, (unpublished manuscript). A. Martin, Unpublished notes on the strong partition relation on ${\omega _1}$.
  • 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
  • Robert M. Solovay, A $\Delta ^{1}_{3}$ coding of the subsets of $\omega _{\omega }$, Cabal Seminar 76โ€“77 (Proc. Caltech-UCLA Logic Sem., 1976โ€“77) Lecture Notes in Math., vol. 689, Springer, Berlin, 1978, pp.ย 133โ€“150. MR 526916
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 03E60, 03E05, 03E15
  • Retrieve articles in all journals with MSC: 03E60, 03E05, 03E15
Additional Information
  • © Copyright 1990 American Mathematical Society
  • 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