Related papers: How much sweetness is there in the universe?
The present paper has three themes. First, we continue the investigations started in Judah, Roslanowski and Shelah \math.LO/9310224 and Roslanowski and Shelah math.LO/9807172, math.LO/9703222, and we investigate the method of norms on…
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…
We deal with an iteration theorem of forcing notion with a kind of countable support of nice enough forcing notion which is proper aleph_2-c.c. forcing notions. We then look at some special cases (Q_D 's preceded by random forcing).
We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A >>Cohen algebra<< is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of…
Using creature technology, we construct families of Suslin ccc non-sweet forcing notions $\mathbb Q$ such that $ZFC$ is equiconsistent with $ZF+$"every set of reals equals a Borel set modulo the $(\leq \aleph_1)$-closure of the null ideal…
We show that for a Suslin ccc forcing notion $\mathbb Q$ adding a Hechler real, ``$\text{ZF}+\text{DC}_{\omega_1}+$all sets of reals are $I_{\mathbb Q,\aleph_0}$-measurable'' implies the existence of an inner model with a measurable…
The feeling that those two forcing notions-Cohen and Random-(equivalently the corresponding Boolean algebras Borel(R)/(meager sets), Borel(R)/(null sets)) are special, was probably old and widespread. A reasonable interpretation is to show…
Let $\kappa$ be an infinite cardinal. Then, forcing with $\mathbb{R}(\kappa)$$\times$$\mathbb{R}(\kappa)$ adds a generic filter for $\mathbb{C}(\kappa);$ where $\mathbb{R}(\kappa)$ and $\mathbb{C}(\kappa)$ are the forcing notions for adding…
Countable tightness may be destroyed by countably closed forcing. We characterize the indestructibility of countable tightness under countably closed forcing by combinatorial statements similar to the ones Tall used to characterize…
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…
In the last decade, huge progress in experimentally measuring and theoretically understanding flavor physics has been achieved. In particular, the accuracy in the determination of the CKM elements has been greatly improved, and a large…
We develop a toolbox for forcing over arbitrary models of set theory without the axiom of choice. In particular, we introduce a variant of the countable chain condition and prove an iteration theorem that applies to many classical forcings…
We prove the following theorem: For a partially ordered set Q such that every countable subset has a strict upper bound, there is a forcing notion satisfying ccc such that, in the forcing model, there is a basis of the meager ideal of the…
We introduce a variant of Martin's axiom, called the grounded Martin's axiom, which asserts that the universe is a ccc forcing extension in which Martin's axiom holds for posets in the ground model. This principle already implies several of…
Ideas from quantum field theory and topology have proved remarkably fertile in suggesting new phenomena in the quantum physics of condensed matter. Here I'll supply some broad, unifying context, both conceptual and historical, for the…
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…
We classify newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. Under the extended Riemann hypothesis for odd real Dirichlet characters, these newforms are finite in number. We produce…
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 prove that a wide class of strongly proper forcing posets have quotients with strong properties. Specifically, we prove that quotients of forcing posets which have simple universal strongly generic conditions on a stationary set of…
We describe a method of building ``nice'' sigma-ideals from Souslin ccc forcing notions. [These notes were written down in 1992, but were not submitted to any journal. In a slightly modified form, they were incorporated to: T. Bartoszynski…