Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A two-cardinal theorem and a combinatorial theorem


Author: Saharon Shelah
Journal: Proc. Amer. Math. Soc. 62 (1977), 134-136
MSC: Primary 02H05; Secondary 04A20, 02H13
MathSciNet review: 0434800
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a new two-cardinal theorem, e.g. $ ({\aleph _\omega },{\aleph _0}) \to ({2^{{\aleph _0}}},{\aleph _0})$. For this we prove a combinatorial theorem.


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

  • [CK] C. C. Chang and H. J. Keisler, Model theory, North-Holland, Amsterdam, 1973.
  • [H Le] J. D. Halpern and A. Lévy, The Boolean prime ideal theorem does not apply the axiom of choice, Proc. Sympos. Pure Math., vol. 13, part 1, Amer. Math. Soc., Providence, R.I., 1971, pp. 83-134. MR 44 #1557.
  • [H La] J. D. Halpern and H. Lauchli, A partition theorem, Trans. Amer. Math. Soc. 124 1966, 360-367. MR 34 #71. MR 0200172 (34:71)
  • [S1] S. Shelah, A two-cardinal theorem, Proc. Amer. Math. Soc. 48 (1975), 207-213. MR 0357105 (50:9573)
  • [S2] -, Coloring without triangles and partition relation, Israel Math. 20 (1975), 1-12. MR 0427073 (55:109)
  • [S3] -, Stability and number of non-isomorphic models (in preparation).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 02H05, 04A20, 02H13

Retrieve articles in all journals with MSC: 02H05, 04A20, 02H13


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0434800-6
PII: S 0002-9939(1977)0434800-6
Keywords: Two-cardinal theorem, partition calculus
Article copyright: © Copyright 1977 American Mathematical Society