Der Beweis eines Satzes von G. Choodnovsky

Aristotelian poetry

“…The best known results are κ + κ → κ n κ <κ for every n ∈ ω and κ + κ → τ κ m for every τ ∈ κ + , m ∈ ω, due to Jones in [10]. The latter is an improvement upon a result of Wolfsdorf from [14].…”

A polarized partition relation for weakly compact cardinals using elementary substructures

“…In this section, we strengthen this result in two ways. First, we weaken the hypothesis that K is an uncountable measurable cardinal to those of K <K = K and K bears a K-dense ideal, and second, we produce a technical improvement in the outcome of the partition relation, providing a new proof of a result of A. Kanamori in [12], which in turn extends a result of K. Wolfsdorf in [14].…”

“…Recall Rowbottom's result that K -> CU)< W whenever It is a normal ultrafilter over K, and then apply Lemma 7. H In [14], K. Wolfsdorf proved that if It is a normal ultrafilter over K, then for any partition / : K + X K -> { 0 , 1 } there are sets A G [K + ] K and B G U and a color i < 2 with f"{A x B) = {/}. That is, Wolfsdorf demonstrated that for each measurable cardinal K and each normal ultrafilter IX over that K .…”

“…To our knowledge, no proof of Cudnovskii's claim is known, though two partial results have been published. In [14], K. Wolfsdorf proved that for any weakly compact K and any a < K + . More recently, Baumgartner and Hajnal have proven in [2] that for any weakly compact K and any fi < K. §2.…”