A Tukey Decomposition Of [mathematical Script Capital P]κλ And The Tree Property For Directed Sets

Mathematical Logic Quarterly 51 (3):305-312 (2005)
  Copy   BIBTEX

Abstract

Generalizing a result of Todorčević, we prove the existence of directed sets D, E such that D ≱ [MATHEMATICAL SCRIPT CAPITAL P]κλ and E ≱ [MATHEMATICAL SCRIPT CAPITAL P]κλ but D × E ≥ [MATHEMATICAL SCRIPT CAPITAL P]κλ in the Tukey ordering. As an application, we show that the tree property for directed sets introduced by Hinnion is not preserved under products.

Categories

Keywords

Reprint years

DOI

10.1002/malq.200410033

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,386

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

A Tukey decomposition of ~k~a~p~p~aLambda and the tree property for directed sets.M. Karato - 2005 - Mathematical Logic Quarterly 51 (3):305.
Universal functions in partial structures.Maurizio Negri - 1992 - Mathematical Logic Quarterly 38 (1):253-268.
On completely nonmeasurable unions.Szymon Żeberski - 2007 - Mathematical Logic Quarterly 53 (1):38-42.
Tychonoff products of compact spaces in ZF and closed ultrafilters.Kyriakos Keremedis - 2010 - Mathematical Logic Quarterly 56 (5):474-487.
Differences of Computably Enumerable Sets.A. Nies & S. Lempp - 2000 - Mathematical Logic Quarterly 46 (4):555-562.
On Computability Theoretic Properties of Structures and Their Cartesian Products.Bakhadyr Khoussainov - 2000 - Mathematical Logic Quarterly 46 (4):467-476.
Mass problems and almost everywhere domination.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):483-492.
The Banach‐Steinhaus theorem for the space ????(ℝ) in constructive analysis.Satoru Yoshida - 2003 - Mathematical Logic Quarterly 49 (3):305-315.
Some observations on the substructure lattice of a 1 ultrapower.Thomas G. McLaughlin - 2010 - Mathematical Logic Quarterly 56 (3):323-330.
Combinatorial Criteria for Ramifiable Ordered Sets.R. Hinnion & O. Esser - 2001 - Mathematical Logic Quarterly 47 (4):539-556.
The wi‐club filter on.Grace Piper - 2009 - Mathematical Logic Quarterly 55 (5):562-568.
The wi-club filter on Pκλ.Grace Piper - 2009 - Mathematical Logic Quarterly 55 (5):562-568.
On superstable groups with residual properties.Abderezak Houcine - 2007 - Mathematical Logic Quarterly 53 (1):19-26.
Tree‐Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
A notion of selective ultrafilter corresponding to topological Ramsey spaces.José G. Mijares - 2007 - Mathematical Logic Quarterly 53 (3):255-267.

Analytics

Added to PP
2013-11-03

Downloads
96 (#176,030)

6 months
2 (#1,232,442)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references