Related papers: Nonproper Products

We introduce the forcing property "almost strong properness" which sits between properness and strong properness. As an application, we introduce a simple forcing with finite conditions to force $\rm MRP$.

For every uncountable regular $\kappa$, we give two examples of proper posets which turn improper in some $\kappa$-closed forcing extension.

We prove a number of results about countable Borel equivalence relations with forcing constructions and arguments. These results reveal hidden regularity properties of Borel complete sections on certain orbits. As consequences they imply…

We give new equivalent characterizations for ideals of Borel type. Also, we prove that the regularity of a product of ideals of Borel type is bounded by the sum of the regularities of those ideals.

We present a simple new method for proving that languages are not regular. We prove the correctness of the method, illustrate the ease of using the method on well-known examples of nonregular languages, and prove two additional theorems on…

We present reasons for developing a theory of forcing notions which satisfy the properness demand for countable models which are not necessarily elementary submodels of some (H(chi), in). This leads to forcing notions which are…

We introduce a simplified framework for ord-transitive models and Shelah's non elementary proper (nep) theory. We also introduce a new construction for the countable support nep iteration.

We look for a parallel to the notion of ``proper forcing'' among lambda-complete forcing notions not collapsing lambda^+ . We suggest such a definition and prove that it is preserved by suitable iterations.

We use Bieri-Strebel invariants to determine when a normal fibre product in the product of two finitely presented groups is finitely presented. We give conditions that imply and in some cases characterize the existence of such finitely…

We introduce more properties of forcing notions which imply that their lambda-support iterations are lambda-proper, where lambda is an inaccessible cardinal. This paper is a direct continuation of section A.2 of math.LO/0210205. As an…

Using forcing with measured creatures we build a universe of set theory in which: (a) every sup-measurable function f:RxR-->R is measurable, and (b) every function f:R-->R is continuous on a non-measurable set. This answers a question of…

I prove forcing preservation theorems for products of definable partial orders preserving the cofinality of the meager or null ideal. Rectangular Ramsey theorems for related ideals follow from the proofs.

We introduce the idea of a coherent adequate set of models, which can be used as side conditions in forcing. As an application we define a forcing poset which adds a square sequence on $\omega_2$ using finite conditions.

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.

We present a systematic study of the method of "norms on possibilities" of building forcing notions with keeping their properties under full control. This technique allows us to answer several open problems, but on our way to get the…

An example of two $\mathbb R$-factorizable groups whose product is not $\mathbb R$-factorizable is constructed. One of these groups is second-countable and the other Lindel\"of to any finite power.

The forcing theorem is the most fundamental result about set forcing, stating that the forcing relation for any set forcing is definable and that the truth lemma holds, that is everything that holds in a generic extension is forced by a…

This article introduces a line of investigation into connections between creature forcings and topological Ramsey spaces. Three examples of sets of pure candidates for creature forcings are shown to contain dense subsets which are actually…

An example of a cocomplete abelian category that is not complete is constructed.

Forcing axioms are generalizations of Baire category principles that allow one to intersect more dense open sets and to do so in a wider variety of circumstances. In this paper we introduce two new forcing axioms related to posets which…