A polarized partition relation and failure of GCH at singular strong limit

• Autorzy: Saharon Shelah
• Języki publikacji: EN

Abstrakty

EN

The main result is that for λ strong limit singular failing the continuum hypothesis (i.e. $2^{λ} > λ^{+}$), a polarized partition theorem holds.

Kategorie tematyczne

• 03E05: Other combinatorial set theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1998
• Tom: 155
• Numer: 2
• Strony: 153-160

Daty

wydano

1998

otrzymano

1995-11-04

poprawiono

1996-10-18

Twórcy

autor

Saharon Shelah

• epartment of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, U.S.A.
• Institute of Mathematics, The Hebrew University, 91 904 Jerusalem, Israel

Bibliografia

• [EHR] P. Erdős, A. Hajnal and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196.
• [BH] J. Baumgartner and A. Hajnal, Polarized partition relations, preprint, 1995.
• [J] T. Jech, Set Theory, Academic Press, New York, 1978.
• [Sh:g] S. Shelah, Cardinal Arithmetic, Oxford Logic Guides 29, Oxford Univ. Press, 1994.
• [Sh 430] S. Shelah, Further cardinal arithmetic, Israel J. Math. 95 (1996), 61-114.
• [Sh 420] S. Shelah, Advances in cardinal arithmetic, in: Finite and Infinite Combinatorics in Sets and Logic, N. W. Sauer et al. (eds.), Kluwer Acad. Publ., 1993, 355-383.
• [Sh 108] S. Shelah, On successors of singular cardinals, in: Logic Colloquium '78 (Mons, 1978), Stud. Logic Found. Math. 97, North-Holland, Amsterdam, 1979, 357-380.