相关论文: Preserving Non-Null with Suslin+ forcing

We define a notion of substitution on colored binary trees that we call substreetution. We show that a fixed point by a substreetution may be (or not) almost periodic, thus the closure of the orbit under $\mathbb{F}_2^+$-action may (or not)…

We consider a class of second order ordinary differential equations describing one-dimensional systems with a quasi-periodic analytic forcing term and in the presence of damping. As a physical application one can think of a…

In this paper we prove that the maximum principle in forcing is equivalent to the axiom of choice. The maximum principle is the property of forcing: p ||- exists x theta(x) iff for some name tau p ||- theta(tau). We also look at three…

In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…

We identify two key conditions that a subset $A$ of a poset $P$ may satisfy to guarantee the transfer of continuity properties from $P$ to $A$. We then highlight practical cases where these key conditions are fulfilled. Along the way we are…

We introduce the notions of over- and under-independence for weakly mixing and (free) ergodic measure preserving actions and establish new results which complement and extend the theorems obtained in [BoFW] and [A]. Here is a sample of…

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

We determine the structure of a finite subset $A$ of an abelian group given that $|2A|<3(1-\epsilon)|A|$, $\epsilon>0$; namely, we show that $A$ is contained either in a "small" one-dimensional coset progression, or in a union of fewer than…

We prove that any countable support iteration formed with posets with $\omega_2$-p.i.c.\ has $\omega_2$-c.c., assuming CH in the ground model and assuming also that $\omega_1$ is not collapsed. This improves earlier results of Shelah by…

We introduce $\ell$-leaky positive semidefinite forcing and the $\ell$-leaky positive semidefinite number of a graph, $Z_{(\ell)}^+{G}$, which combines the positive semidefinite color change rule with the addition of leaks to the graph.…

We introduce the notion of non-lc ideal sheaves. It is an analogue of the notion of multiplier ideal sheaves. We establish the restriction theorem, which seems to be the most important property of non-lc ideal sheaves.

We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a linear process in which the coefficients are of the form $a_i=i^{-1}\ell(i)$ with $\ell$ being a slowly varying function at the infinity and the innovations are independent and identically distributed…

A stochastic forest model of young and old age class trees is studied. First, we prove existence, uniqueness and boundedness of global nonnegative solutions. Second, we investigate asymptotic behavior of solutions by giving a sufficient…

Let G be any additive abelian group with cyclic torsion subgroup, and let A, B and C be finite subsets of G with cardinality n>0. We show that there is a numbering {a_i}_{i=1}^n of the elements of A, a numbering {b_i}_{i=1}^n of the…

Let $F$ be a field and a finite $A\subset F$ be sufficiently small in terms of the characteristic $p$ of $F$ if $p>0$. We strengthen the "threshold" sum-product inequality $$|AA|^3 |A\pm A|^2 \gg |A|^6\,,\;\;\;\;\mbox{hence} \;\;…

This is an exposition of much of Sections VI.3 and XVIII.3 of "Proper and Improper Forcing", including preservations for "no random reals over V", "reals of V form a non-meager set", "every dense open set contains a dense open set in V",…

In this paper we prove a basic theorem which says that if f : F_p^n -> [0,1] has the property that ||f^||_(1/3) is not too ``large''(actually, it also holds for quasinorms 1/2-\delta in place of 1/3), and E(f) = p^{-n} sum_m f(m) is not too…

We prove a variation of Easton's lemma for strongly proper forcings, and use it to prove that, unlike the stronger principle $\textsf{IGMP}$, $\textsf{GMP}$ together with $2^\omega \le \omega_2$ is consistent with the existence of an…

Given a linearly ordered set I, every surjective map p: A --> I endows the set A with a structure of set of preferences by "replacing" the elements of I with their inverse images via p considered as "balloons" (sets endowed with an…