# More results in polychromatic Ramsey theory

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 1004-1016
- ISSN: 2391-5455

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topUri Abraham, and James Cummings. "More results in polychromatic Ramsey theory." Open Mathematics 10.3 (2012): 1004-1016. <http://eudml.org/doc/269526>.

@article{UriAbraham2012,

abstract = {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 \rightarrow ^\{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 $ .},

author = {Uri Abraham, James Cummings},

journal = {Open Mathematics},

keywords = {Polychromatic Ramsey theory; Proper forcing; Models as side conditions; polychromatic Ramsey theory; proper forcing; models as side conditions},

language = {eng},

number = {3},

pages = {1004-1016},

title = {More results in polychromatic Ramsey theory},

url = {http://eudml.org/doc/269526},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Uri Abraham

AU - James Cummings

TI - More results in polychromatic Ramsey theory

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 1004

EP - 1016

AB - 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 \rightarrow ^{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 $ .

LA - eng

KW - Polychromatic Ramsey theory; Proper forcing; Models as side conditions; polychromatic Ramsey theory; proper forcing; models as side conditions

UR - http://eudml.org/doc/269526

ER -

## References

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- [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 Zbl0532.03023
- [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 Zbl0592.03037

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