Stephen Jackson

activity

20172020

most citedEquivalence of the Rothberger and

2

-Rothberger Games for Hausdorff Spaces

2 citations · 4 across the 5 of their papers we have counts for

collaborators

9 papers

math.DS2020

A non-Borel special alpha-limit set in the square

Steve Jackson, Bill Mance, Samuel Roth

We consider the complexity of special $α$ -limit sets, a kind of backward limit set for non-invertible dynamical systems. We show that these sets are always analytic, but not necess…

math.LO2020

Hausdorff Dimension Regularity Properties and Games

Logan Crone, Lior Fishman, Stephen Jackson

The Hausdorff $δ$ -dimension game was introduced by Das, Fishman, Simmons and {Urba{ń}ski} and shown to characterize sets in $R^{d}$ having Hausdorff dimension $\leq δ$ . We i…

math.LO2020

Equivalence Relations and Determinacy

Logan Crone, Lior Fishman, Stephen Jackson

We introduce the notion of $(Γ, E)$ -determinacy for $Γ$ a pointclass and $E$ an equivalence relation on a Polish space $X$ . A case of particular interest is the case when $E = E_{G}$ is…

math.LO2019

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…

math.LO2019

The Destruction of the Axiom of Determinacy by Forcings on $R$ when $Θ$ is Regular

William Chan, Stephen Jackson

$ZF + AD$ proves that for all nontrivial forcings $P$ on a wellorderable set of cardinality less than $Θ$ , $1_{P} ⊩_{P} \neg AD$ . $…

math.LO2019★ 2 cited

Cardinality of Wellordered Disjoint Unions of Quotients of Smooth Equivalence Relations