We show that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. The proof uses ideas of Moore from [11] and the notion of a relativized trace function on pairs of ordinals.

We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize… (More)

We present two results which shed some more light on the deep connection between ZFA and the standard ZF set theory: First of all we refine a result of Forti and Honsell (see [5]) in order to prove… (More)

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a… (More)

Hearing loss and tinnitus are frequently encountered in ENT patients and usually require complementary investigations such as audiogram, auditive evoked potentials, CT scan, MRI... One recent… (More)

Schanuel’s conjecture states that the transcendence degree over Q of the 2n-tuple (λ1, . . . , λn, e λ1 , . . . , en) is at least n for all λ1, . . . , λn ∈ C which are linearly independent over Q;… (More)

There are several examples in the literature showing that compactness-like properties of a cardinal κ cause poor behavior of some generic ultrapowers which have critical point κ (Burke [1] when κ is… (More)

Intersection types discipline allows to define a wide variety of models for the type free lambda-calculus, but the Curry-Howard isomorphism breaks down for this kind of type systems. In this paper we… (More)