35 citations · 69 across the 6 of their papers we have counts for
6 papers
The mouse set conjecture for sets of reals
Grigor Sargsyan, John Steel
Recall that the Mouse Set Conjecture says that under AD++V=L(P(R)), a real is ordinal definable if and only if it belongs to an iterable mouse. The Mouse Set Conjecture for sets of…
Comparison of fine structural mice via coarse iteration
Farmer Schlutzenberg, John R. Steel
Let M be a fine structural mouse. Let D be a fully backgrounded L[E]-construction computed inside an iterable coarse premouse S. We describe a process comparing M with D, through f…
Square principles in Pmax extensions
Andrés Eduardo Caicedo, Paul Larson, Grigor Sargsyan +3
By forcing with over strong models of determinacy, we obtain models where different square principles at and fail. In particular, we obtain a mod…
Martin's conjecture, arithmetic equivalence, and countable Borel equivalence relations
Andrew Marks, Theodore Slaman, John Steel
There is a fascinating interplay and overlap between recursion theory and descriptive set theory. A particularly beautiful source of such interaction has been Martin's conjecture o…
The covering lemma up to a Woodin cardinal
William J. Mitchell, Ernest Schimmerling, John R. Steel
A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be th…
How to win some simple iteration games
Alessandro Andretta, John R. Steel
We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G+, which is somewhat stronger than G but weaker than the full i…