A polarized partition relation for cardinals of countable cofinality

Author:
Albin L. Jones

Journal:
Proc. Amer. Math. Soc. **136** (2008), 1445-1449

MSC (2000):
Primary 03E05, 05D10; Secondary 05A18

Published electronically:
November 30, 2007

MathSciNet review:
2367118

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if and , then

**1.**J. Baumgartner and A. Hajnal,*A proof (involving Martin’s axiom) of a partition relation*, Fund. Math.**78**(1973), no. 3, 193–203. MR**0319768****2.**G. V. Čudnovskiĭ,*Combinatorial properties of compact cardinals*, Infinite and finite sets (Colloq., Keszthely, 1973; dedicated to P. Erdős on his 60th birthday), Vol. I, North-Holland, Amsterdam, 1975, pp. 289–306. Colloq. Math. Soc. János Bolyai, Vol. 10. MR**0371655****3.**P. Erdős, A. Hajnal, and R. Rado, Partition relations for cardinal numbers, Acta Math. Acad. Sci. Hungar. 16 (1965), 93-196.**4.**P. Erdös and R. Rado,*A partition calculus in set theory*, Bull. Amer. Math. Soc.**62**(1956), 427–489. MR**0081864**, 10.1090/S0002-9904-1956-10036-0

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Additional Information

**Albin L. Jones**

Affiliation:
2153 Oakdale Rd., Pasadena, Maryland 21122

Email:
alj@mojumi.net

DOI:
http://dx.doi.org/10.1090/S0002-9939-07-09143-5

Keywords:
Transfinite cardinal,
countable cofinality,
elementary substructure,
transfinite ordinal,
polarized partition relation,
Ramsey theory,
regular cardinal,
singular cardinal

Received by editor(s):
October 13, 2006

Received by editor(s) in revised form:
February 15, 2007

Published electronically:
November 30, 2007

Communicated by:
Julia Knight

Article copyright:
© Copyright 2007
Albin L. Jones