A Polarized Partition Relation for Weakly Compact Cardinals Using Elementary Substructures

Journal of Symbolic Logic 71 (4):1342 - 1352 (2006)

Abstract
We show that if κ is a weakly compact cardinal, then $\left( \matrix \kappa ^{+} \\ \kappa\endmatrix \right)\rightarrow \left(\left( \matrix \alpha \\ \kappa \endmatrix \right)_{m}\left( \matrix \kappa ^{n} \\ \kappa \endmatrix \right)_{\mu}\right)^{1,1}$ for any ordinals α < κ⁺ and µ < κ, and any finite ordinals m and n. This polarized partition relation represents the statement that for any partition $\kappa \times \kappa ^{+}=\underset i<m\to{\bigcup }K_{i}\cup \underset j<\mu \to{\bigcup }L_{j}$ of κ × κ⁺ into m + µ pieces either there are A ∈ [κ]κ, B ∈ [κ⁺]α, and i < m with A × B ⊆ Ki or there are C ∈ [κ]κ, D ∈ [κ⁺]α, and j < μ with C × D ⊆ Lj. Related results for measurable and almost measurable κ are also investigated. Our proofs of these relations involve the use of elementary substructures of set models of large fragments of ZFC
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2178/jsl/1164060459
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 42,433
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

In Memoriam: James Earl Baumgartner.J. A. Larson - 2017 - Archive for Mathematical Logic 56 (7-8):877-909.

Add more citations

Similar books and articles

Polarized Partition Relations.James E. Baumgartner & Andras Hajnal - 2001 - Journal of Symbolic Logic 66 (2):811-821.
A Polarized Partition Relation Using Elementary Substructures.Albin L. Jones - 2000 - Journal of Symbolic Logic 65 (4):1491-1498.
Spector Forcing.J. M. Henle - 1984 - Journal of Symbolic Logic 49 (2):542-554.
Strong Compactness and Stationary Sets.John Krueger - 2005 - Journal of Symbolic Logic 70 (3):767 - 777.
A Baire-Type Theorem for Cardinals.Kurt Wolfsdorf - 1983 - Journal of Symbolic Logic 48 (4):1082-1089.
Two Weak Consequences of 0#. [REVIEW]M. Gitik, M. Magidor & H. Woodin - 1985 - Journal of Symbolic Logic 50 (3):597 - 603.
Extender Based Forcings.Moti Gitik & Menachem Magidor - 1994 - Journal of Symbolic Logic 59 (2):445-460.
Abstract Logic and Set Theory. II. Large Cardinals.Jouko Väänänen - 1982 - Journal of Symbolic Logic 47 (2):335-346.
On Measurable Limits of Compact Cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
On Some Small Cardinals for Boolean Algebras.Ralph Mckenzie & J. Donald Monk - 2004 - Journal of Symbolic Logic 69 (3):674-682.

Analytics

Added to PP index
2010-08-24

Total views
12 ( #631,740 of 2,255,414 )

Recent downloads (6 months)
1 ( #985,775 of 2,255,414 )

How can I increase my downloads?

Downloads

My notes

Sign in to use this feature