A theorem of Woodin states that the existence of a proper class of Woodin cardinals implies that the theory of the inner model L(ℝ) cannot be changed by set forcing. The Axiom of Determinacy is part… Expand

How many permutations of the natural numbers are needed so that every conditionally convergent series of real numbers can be rearranged to no longer converge to the same sum? We define the… Expand

These principles for guessing clubs in the generalized club filter on Pκλ are shown to be weaker than classical diamond principles but often serve as sufficient substitutes.Expand

It is shown that it is possible to force that the canonical function game is not determined, and the relationship between this result and Σ22 absoluteness, cardinality spectra and Π2 maximality for H(ω2) relative to the Continuum Hypothesis is discussed.Expand

Woodin has demonstrated that, in the presence of large cardinals, there is a single model of ZFC which is maximal for Π2-sentences over the structure (H(ω2), ∈, NSω1), in the sense that its (H(ω2),… Expand

We consider three combinatorial topics appearing in Gödel’s manuscript Some considerations leading to the probable conclusion that the true power of the continuum is א2. These statements concern… Expand