Related papers: Understanding preservation theorems: omega-omega b…
The purpose of this article is to prove that the forcing axiom for completely proper forcings is inconsistent with the Continuum Hypothesis. This answers a longstanding problem of Shelah. The corresponding completely proper forcing which…
We give some sufficient and necessary conditions on a forcing notion Q for preserving the forcing notion ([omega]^{aleph_0},supseteq^*) is proper. They cover many reasonable forcing notions.
In this paper we analyse some notions of amoeba for tree forcings. In particular we introduce an amoeba-Silver and prove that it satisfies quasi pure decision but not pure decision. Further we define an amoeba-Sacks and prove that it…
We show that Shelah cardinals are preserved under the canonical $GCH$ forcing notion. We also show that if $GCH$ holds and $F:REG\rightarrow CARD$ is an Easton function which satisfies some weak properties, then there exists a cofinality…
In this work, various versions of the so-called Omega-Lemma are provided, which ensure differentiability properties of pushforwrds between spaces of C^r-sections (or compactly supported C^r-sections) in vector bundles over…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
This paper presents the main results in my Ph.D. thesis. In what follows several proofs of SCH are presented introducing a family of covering properties which implies both SCH and the failure of various forms of square. These covering…
We investigate the problem of when $\leq\lambda$--support iterations of $<\lambda$--complete notions of forcing preserve $\lambda^+$. We isolate a property -- {\em properness over diamonds} -- that implies $\lambda^+$ is preserved and show…
Shelah considered a certain version of Strong Chang's Conjecture, which we denote $\text{SCC}^{\text{cof}}$, and proved that it is equivalent to several statements, including the assertion that Namba forcing is semiproper. We introduce an…
We give an exposition of an iteration theorem for iterating $(<\lambda)$-closed stationary $\lambda^+$-cc forcing with supports of size $<\lambda$ and preserving these two properties. We discuss the relation of this theorem with other…
In this paper we review Shelah's strong covering property and its applications. We also extend some of the results of Shelah and Woodin on the failure of $CH$ by adding a real.
We investigate the relationship between the Eklof-Mekler-Shelah Construction Principle for a variety of algebras $\mathbf{V}$ and the question of superstability of the free objects in $\mathbf{V}$, denoted as $\mathcal{F}_\mathbf{V}$. We…
The superamalgamation property is a strong form of the amalgamation property which applies to ordered structures; it has found many applications in algebraic logic. We show that superamalgamation has some interest also from the pure…
We prove that the Sacks forcing collapses the continuum onto the dominating number d, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses omega_2 then it forces…
This thesis develops the theory of bundle gerbes and examines a number of useful constructions in this theory. These allow us to gain a greater insight into the structure of bundle gerbes and related objects. Furthermore they naturally lead…
This was supposed to be an appendix to the book "Non-structure", and probably will be if it materializes. It presents relevant material, sometimes new, which was used in works which were supposed to be part of that book. In section 1 we…
Roughly speaking, a system is said to be robust if it can resist disturbances and still function correctly. For instance, if the requirement is that the temperature remains in an allowed range $[l,h]$, then a system that remains in a range…
It is pointed out that current conservation alone does not suffice to prove Hara's theorem as it was claimed recently. By explicit calculation we show that the additional implicit assumption made in such "proofs" is that of a sufficiently…
We develop the model theory of omega-stable K-loops and 'sym\'etrons'. Continuing Poizat's seminal work, we notably establish an appropriate version of the indecomposability theorem and we adapt Lascar's analysis to this context. -- Nous…
Iwasa investigated the preservation of various covering properties of opological spaces under Cohen forcing. By improving the argument in Iwasa's paper, we prove that the Rothberger property, the Menger property and selective screenability…