2 citations · 2 across the 6 of their papers we have counts for
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The Borel partition spectrum at successors of singular cardinals
Will Brian
Assuming that does not exist, we prove that if there is a partition of into Borel sets, then there is also a partition of into $\alep…
Combinatorial and number-theoretic properties of generic reals
Will Brian, Mohammad Golshani
We discuss some properties of Cohen and random reals. We show that they belong to any definable partition regular family, and hence they satisfy most "largeness" properties studied…
Covering versus partitioning with Polish spaces
Will Brian
Given a completely metrizable space , let denote the smallest possible size of a partition of into Polish spaces, and the smallest po…
The independence of GCH and a combinatorial principle related to Banach-Mazur games
Will Brian, Alan Dow, Saharon Shelah
It was proved recently that Telgársky's conjecture, which concerns partial information strategies in the Banach-Mazur game, fails in models of . The proof int…
Telgarsky's conjecture may fail
Will Brian, Alan Dow, David Milovich +1
Telgársky's conjecture states that for each , there is a topological space such that in the Banach-Mazur game on , the player {\scriptsize NONEMPTY} has…
Small cardinals and small Efimov spaces
Will Brian, Alan Dow
We introduce and analyze a new cardinal characteristic of the continuum, the \emph{splitting number of the reals}, denoted . This number is connected to Ef…