4 papers
The super tree property at the successor of a singular
Sherwood Hachtman, Dima Sinapova
For an inaccessible cardinal , the super tree property (ITP) at holds if and only if is supercomact. However, just like the tree property, it can hold at successor cardi…
Scattered Sentences have Few Separable Randomizations
Uri Andrews, Isaac Goldbring, Sherwood Hachtman +2
In the paper "Randomizations of Scattered Sentences", Keisler showed that if Martin's axiom for aleph one holds, then every scattered sentence has few separable randomizations, and…
Determinacy separations for class games
Sherwood Hachtman
We show, assuming weak large cardinals, that in the context of games played in a proper class of moves, clopen determinacy is strictly weaker than open determinacy. The proof amoun…
determinacy and monotone induction
Sherwood Hachtman
Building on recent work of Philip Welch, we prove that (lightface) determinacy is equivalent to the existence of a wellfounded model satisfying the axiom scheme of (boldfac…