Displaying similar documents to “The uncountable spectra of countable theories.”

More results in polychromatic Ramsey theory

Uri Abraham, James Cummings (2012)

Open Mathematics

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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 ω 2 → p o l y ( α ) ℵ 0 - b d d 2 for every α <ω 2; (2) 2ω = ω 2 and ω 2 ↛ p o l y ( ω 1 ) 2 - b d d 2 .

Another proof of a result of Jech and Shelah

Péter Komjáth (2013)

Czechoslovak Mathematical Journal

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Shelah’s pcf theory describes a certain structure which must exist if ℵ ω is strong limit and 2 ℵ ω > ℵ ω 1 holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that...