Countable partition ordinals

被引：4

作者：

Schipperus, Rene ^{[1
]}

机构：

[1] Univ Calgary, Dept Math & Stat, Calgary, AB T2N 1N4, Canada

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2010年 / 161卷 / 10期

关键词：

Ramsey theory; Set theory; Ordinals; Martin's axiom; Partition calculus;

D O I：

10.1016/j.apal.2009.12.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The structure of ordinals of the form omega(omega beta) for countable beta is studied. The main result is: Theorem 1. If beta < omega(1) is the sum of one or two indecomposable ordinals, then omega(omega beta) -> (omega(omega beta), 3)(2). Also an example is given to show that alpha -> (alpha, 3)(2) need not imply alpha (alpha, n)(2) for all n < omega. (C) 2010 Published by Elsevier B.V.

引用

页码：1195 / 1215

页数：21

共 9 条

[1] Chang, 1972, J COMBINATORIAL TH A, V12, P396, DOI DOI 10.1016/0097-3165(72)90105-7
[2] Negative partition relations for ordinals ωωα
Darby, C
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1999, 76 (02) : 205 - 222
[3] Larson, 1974, FUND MATH, V82, P357, DOI DOI 10.4064/FM-82-4-357-361
[4] Larson J.A., 1973, Ann. Math. Log., V6, P129, DOI [DOI 10.1016/0003-4843(73)90006-5, /10.1016/0003-4843(73)90006-5]
[5] An ordinal partition avoiding pentagrams
Larson, JA
[J]. JOURNAL OF SYMBOLIC LOGIC, 2000, 65 (03) : 969 - 978
[6] Nash-Williams C. St. J. A., 1965, P CAMBRIDGE PHIL SOC, V61, P33
[7] SAUER NW, 1993, FINITE INFINITE COMB
[8] Specker Ernst., 1957, Comment. Math. Helv, V31, P302
[9] Williams N. H., 1977, COMBINATORIAL SET TH

← 1 →