More results in polychromatic Ramsey theory

• Autorzy: Uri Abraham , James Cummings
• Języki publikacji: EN

Abstrakty

EN

We study polychromatic Ramsey theory with a focus on colourings of [ω 2]2. We show that in the absence of GCH there is a wide range of possibilities. In particular each of the following is consistent relative to the consistency of ZFC: (1) 2ω = ω 2 and $\omega _2 \to ^{poly} (\alpha )_{\aleph _0 - bdd}^2 $ for every α <ω 2; (2) 2ω = ω 2 and $\omega _2 \nrightarrow ^{poly} (\omega _1 )_{2 - bdd}^2 $ .

Słowa kluczowe

EN

Polychromatic Ramsey theory; Proper forcing; Models as side conditions

Kategorie tematyczne

• 03E02: Partition relations
• 03E35: Consistency and independence results

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 1004-1016

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Uri Abraham

• Ben-Gurion University

autor

James Cummings

• Carnegie Mellon University

Bibliografia

• [1] Abraham U., Cummings J., Smyth C., Some results in polychromatic Ramsey theory, J. Symbolic Logic, 2007, 72(3), 865–896 http://dx.doi.org/10.2178/jsl/1191333845
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• [4] Galvin F., letters to S. Todorčevic, cited in: Todorčevic S., Forcing positive partition relations, Trans. Amer. Math. Soc., 1983, 280(2), 703–720
• [5] Koszmider P., On strong chains of uncountable functions, Israel J. Math., 2000, 118, 289–315 http://dx.doi.org/10.1007/BF02803525
• [6] Shelah S., Zapletal J., Embeddings of Cohen algebras, Adv. Math., 1997, 126(2), 93–118 http://dx.doi.org/10.1006/aima.1996.1597
• [7] Todorčević S., Forcing positive partition relations, Trans. Amer. Math. Soc., 1983, 280(2), 703–720
• [8] Todorčević S., A note on the proper forcing axiom, In: Axiomatic Set Theory, Boulder, June 19–25, 1983, Contemp. Math. 31, American Mathematical Society, Providence, 1984
• [9] Todorčević S., Directed sets and cofinal types, Trans. Amer. Math. Soc., 1985, 290(2), 711–723

Identyfikatory

DOI

10.2478/s11533-012-0037-3