2 citations · 2 across the 3 of their papers we have counts for
5 papers
Hausdorff Dimension Regularity Properties and Games
Logan Crone, Lior Fishman, Stephen Jackson
The Hausdorff -dimension game was introduced by Das, Fishman, Simmons and {Urba{ń}ski} and shown to characterize sets in having Hausdorff dimension . We i…
Equivalence Relations and Determinacy
Logan Crone, Lior Fishman, Stephen Jackson
We introduce the notion of -determinacy for a pointclass and an equivalence relation on a Polish space . A case of particular interest is the case when is…
The Measure Game
Logan Crone, Lior Fishman, Stephen Jackson +2
We study a game first introduced by Martin (actually we use a slight variation of this game) which plays a role for measure analogous to the Banach-Mazur game for category. We firs…
Equivalence of the Rothberger and -Rothberger Games for Hausdorff Spaces
Logan Crone, Lior Fishman, Nathaniel Hiers +1
We prove that in any Hausdorff space, the Rothberger game is equivalent to the -Rothberger game, i.e. the game in which player II chooses open sets in each move. This result…
Determinacy of Schmidt's Game and Other Intersection Games
Logan Crone, Lior Fishman, Stephen Jackson
Schmidt's game, and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory.…