Related papers: Adding $\aleph_\omega$ many Cohen reals

We study combinatorial principles we call Homogeneity Principle HP(\kappa) and Injectivity Principle IP(\kappa,\lambda) for regular \kappa>\aleph_1 and \lambda\leq\kappa which are formulated in terms of coloring the ordinals <\kappa by…

Shelah has provided sufficient conditions for an $L_{\omega_1, \omega}$-sentence $\psi$ to have arbitrarily large models and for a Morley-like theorem to hold of $\psi$. These conditions involve structural and set-theoretic assumptions on…

In this paper we show that if $A$ is a subset of Chen primes with positive relative density $\alpha$, then $A+A$ must have positive upper density at least $c\alpha e^{-c^\prime\log(1/\alpha)^{2/3}(\log\log(1/\alpha))^{1/3}}$ in the natural…

We show the existence of and explicitly construct generic polynomials for various groups, over fields of positive characteristic. The methods we develop apply to a broad class of connected linear algebraic groups defined over finite fields…

In this work we use a notion of rank first introduced by James Baumgartner and Peter Dordal and later developed independently by the third author to show that adding a Hechler real has strong combinatorial consequences. We prove: 1)…

We will show how the refined holomorphic anomaly equation obeyed by the Nekrasov partition function at generic $\epsilon_1,\epsilon_2$ values becomes compatible, in a certain two parameters expansion, with the assumption that both…

This paper shows that if $R$ is a homomorphic image of a Cohen-Macaulay local ring, then $R$-module $M$ is sequentially generalized Cohen-Macaulay if and only if the difference between Hilbert coefficients and arithmetic degrees for all…

We consider homogeneity properties of Boolean algebras that have nonprincipal ultrafilters which are countably generated.It is shown that a Boolean algebra B is homogeneous if it is the union of countably generated nonprincipal ultrafilters…

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…

We discuss ways of adjoining perfect sets of mutually generic random reals. In particular, we show that if V \sub W are models of ZFC and W contains a dominating real over V, then W[r], where r is random over W, contains a perfect tree of…

We consider some special type extensions of an arbitrary Lie algebra ${\cal G}$, arising in the theory of Lie-Poisson structures over $({\cal G}^*)^n$, where ${\cal G}^*$ is the dual of ${\cal G}$. We show that some classes of these…

The Mordell--Lang conjecture for abelian varieties states that the intersection of an algebraic subvariety $X$ with a subgroup of finite rank is contained in a finite union of cosets contained in $X$. In this article, we prove a uniform…

We discuss the effect of adding a single real (for various forcing notions adding reals) on cardinal invariants associated with the continuum (like the unbounding or the dominating number or the cardinals related to measure and category on…

We show that it is consistent to have an uncountable sequential group of intermediate sequential order while no countable such groups exist. This is proved by adding $\omega_2$ Cohen reals to a model of $\diamondsuit$.

In this paper, we introduce the notion of "extension" of a toric variety and study its fundamental properties. This gives rise to infinitely many toric varieties with a special property, such as being set theoretic complete intersection or…

We investigate game-theoretic properties of selection principles related to weaker forms of the Menger and Rothberger properties. For appropriate spaces some of these selection principles are characterized in terms of a corresponding game.…

We generalize Dirichlet's diophantine approximation theorem to approximating any real number $\alpha$ by a sum of two rational numbers $\frac{a_1}{q_1} + \frac{a_2}{q_2}$ with denominators $1 \leq q_1, q_2 \leq N$. This turns out to be…

We prove (ZF+DC) e.g. : if mu =|H(mu)| then mu^+ is regular non measurable. This is in contrast with the results for mu = aleph_{omega} on measurability see Apter Magidor [ApMg]

We show that the algebraic invariants multiplicity and depth of a graded ideal in the polynomial ring are closely connected to the fan structure of its generic tropical variety in the constant coefficient case. Generically the multiplicity…

We review and analyse techniques from the literature for extending a normed algebra, A to a normed algebra, B, so that B has interesting or desirable properties which A may lack. For example, B might include roots of monic polynomials over…