Related papers: Some Natural Internal Forcing Schemata Extending Z…

It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.

We give a model where there is a ccc Souslin forcing which does not satisfy the Knaster condition. Next, we present a model where there is a sigma-linked not sigma-centered Souslin forcing such that all its small subsets are sigma-centered…

We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles,…

Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In this paper I…

We propose Equivariant ZFA with Choice as a foundation for nominal techniques that is stronger than ZFC and weaker than FM, and why this may be particularly helpful in the context of automated reasoning.

We prove two general results about the preservation of extendible and $C^{(n)}$-extendible cardinals under a wide class of forcing iterations (Theorems 5.4 and 7.5). As applications we give new proofs of the preservation of Vop\v{e}nka's…

This article continues Roslanowski and Shelah math.LO/9906024 and 1105.6049 We introduce here yet another property of (<lambda)-strategically complete forcing notions which implies that their lambda-support iterations do not collapse…

A new renormalization scheme for theories with nontrivial internal symmetry is proposed. The scheme is regularization independent and respects the symmetry requirements.

The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…

We consider kinetic systems and prove their stability working in weighted spaces in which the systems are symmetric. We prove stability for various explicit and implicit semi-discrete and fully discrete schemes. The applications include…

The bounded proper forcing axiom BPFA is the statement that for any family of aleph_1 many maximal antichains of a proper forcing notion, each of size aleph_1, there is a directed set meeting all these antichains. A regular cardinal kappa…

It is well-known that the Continuum Hypothesis (CH) is independent of the other axioms of Zermelo-Fraenkel set theory with choice (ZFC). This raises the question of whether an intuitive justification exists for CH as an additional axiom, or…

In this work, we are interested in the controllability of Vlasov-Poisson systems in the presence of an external force field (namely a bounded force field or a magnetic field), by means of a local interior control. We are able to extend the…

We consider here Easton support iterations of Prikry type forcing notions. New ways of constructing normal ultrafilters in extensions are presented. It turns out that, in contrast with other supports, seemingly unrelated measures or…

Natural protein sequences contain a record of their history. A common constraint in a given protein family is the ability to fold to specific structures, and it has been shown possible to infer the main native ensemble by analyzing…

A central theme in set theory is to find universes with extreme, well-understood behaviour. The case we are interested in is assuming GCH and has a strong forcing axiom of higher order than usual. Instead of "for every suitable forcing…

The effectful forcing technique allows one to show that the denotation of a closed System T term of type $(\iota \to \iota) \to \iota$ in the set-theoretical model is a continuous function $(\mathbb{N} \to \mathbb{N}) \to \mathbb{N}$. For…

We examine the existence (and mostly non-existence) of fresh sets in commonly used iterations of Prikry type forcing notions. Results of [4] are generalized. As an application, a question of a referee of [9] is answered. In addition…

We extend to the critical (intermediate) regularity several results concerning rigidity for centralizers and group actions on the interval.

The Necessary Maximality Principle for c.c.c. forcing asserts that any statement about a real in a c.c.c. extension that could become true in a further c.c.c. extension and remain true in all subsequent c.c.c. extensions, is already true in…