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Category Archives: Expository
Bell’s theorem on the cardinal invariant
In this post, we shall provide a proof to a famous theorem of Murray Bell stating that
The
Here is an elementary proof of (the finitary version of) the
Posted in Blog, Expository, Surprisingly short
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Prikry Forcing
Recall that the chromatic number of a (symmetric) graph
Shelah’s approachability ideal (part 2)
In a previous post, we defined Shelah’s approachability ideal
Posted in Blog, Expository, Open Problems
Tagged approachability ideal, Club Guessing
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The uniformization property for
Given a subset of a regular uncountable cardinal
The uniformization property for
Given a subset of a regular uncountable cardinal
The Engelking-Karlowicz theorem, and a useful corollary
Theorem (Engelking-Karlowicz, 1965). For cardinals
Kurepa trees and ineffable cardinals
Recall that
Variations on diamond
Jensen’s diamond principle has many equivalent forms. The translation between these forms is often straight-forward, but there is one form whose equivalence to the usual form is somewhat surprising, and Devlin’s translation from one to the other, seems a little … Continue reading
The P-Ideal Dichotomy and the Souslin Hypothesis
John Krueger is visiting Toronto these days, and in a conversation today, we asked ourselves how do one prove the Abraham-Todorcevic theorem that PID implies SH. Namely, that the next statement implies that there are no Souslin trees: Definition. The … Continue reading
