8 papers
All Ordinals are Cop-Robber Ordinals
Jorge Cruz Chapital, Tomáš Flídr, Maria-Romina Ivan
The game of cops and robbers, played on a fixed graph , is a two-player game, where the cop and the robber (the players) take turns in moving to adjacent vertices. The game fini…
Forcing Axioms and construction schemes
Jorge Antonio Cruz Chapital, Osvaldo Guzman, Stevo Todorcevic
We continue the development of the theory of construction schemes over as introduced by the third author by studying their relation with forcing axioms. Formally, we introduc…
There may be an -entangled set but no -entangled sets
Jorge Antonio Cruz Chapital
In this paper we show that for every , the statement "there is an -entangled set, but there are no -entangled sets" is consistent. We also prove some…
-barely independent families and Tukey types of ultrafilters
Jorge Antonio Cruz Chapital
Given two infinite cardinals and , we introduce and study the notion of a -barely independent family over We provide some conditions under which these types of famil…
Game-theoretic variants of splitting number
Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi +1
We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number since the corresponding cardinal in…
On construction schemes: building the uncountable from finite pieces
Jorge Antonio Cruz Chapital
In this Phd. thesis, a structural analysis of construction schemes is developed. The importance of this study will be justified by constructing several distinct combinatorial objec…