We study the class of analytic ideals on the set of natural numbers ordered under Tukey reducibility. We consider mostly structural issues: characterization of ideals which are Tukey above w”‘,… (More)

We describe deterministic algorithms which for a given depth-2 circuit $F$ approximate the probability that on a random input $F$ outputs a specific value $\alpha$. Our approach gives an algorithm… (More)

We describe efficient constructions of small probability spaces that approximate the independent distribution for general random variables. Previous work on efficient constructions concentrate on… (More)

We show that the bounded proper forcing axiom BPFA implies that there is a well-ordering of P(ω1) which is Δ1 definable with parameter a subset of ω1. Our proof shows that if BPFA holds then any… (More)

We develop several quasi-polynomial-time deterministic algorithms for approximating the fraction of truth assignments that satisfy a disjunctive normal form formula. The most efficient algorithm… (More)

We describe efficient constructions of small probability spaces that approximate the joint distribution of general random variables. Previous work on efficient constructions concentrate on… (More)

Prikry asked if it is relatively consistent with the usual axioms of ZFC that every nontrivial ccc forcing adds either a Cohen or a random real. Both Cohen and random reals have the property that… (More)

We show that for an atomless complete Boolean algebra 8 of density < 2N°, the Banach-Mazur, the split and choose, and the Ulam game on S are equivalent. Moreover, one of the players has a winning… (More)

In [13] it was demonstrated that the Proper Forcing Axiom implies that there is a five element basis for the class of uncountable linear orders. The assumptions needed in the proof have consistency… (More)