83 citations · 293 across the 29 of their papers we have counts for
8 papers · 1 filter
Schmidt's Game and Vitali Sets
James Atchley, Lior Fishman, Stephen Jackson +2
While many types of non-measurable sets are never -winning in the sense of Schmidt's game, we show that this is not the case for certain Vitali sets. Our main theorems show…
Intersection Games and Bernstein Sets
James Atchley, Lior Fishman, Saisneha Ghatti
The Banach-Mazur game, Schmidt's game and McMullen's absolute winning game are three quintessential intersection games. We investigate their determinacy on the real line when the t…
The no- McMullen game and the perfect set property
Logan Crone, Lior Fishman, Stephen Jackson
Given a target set and a real number , McMullen introduced the notion of being an absolutely -winning set. This involves a two player g…
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…
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.…
Determinacy and indeterminacy of games played on complete metric spaces
Lior Fishman, Tue Ly, David S. Simmons
Schmidt's game is a powerful tool for studying properties of certain sets which arise in Diophantine approximation theory, number theory, and dynamics. Recently, many new results h…