English
Related papers

Related papers: On reflection of stationary sets in P_kappa lambda

200 papers

We investigate stability of replica symmetry breaking solutions in generalized $p$-spin models. It is shown that the kind of the transition to the one-step replica symmetry breaking state depends not only on the presence or absence of the…

Disordered Systems and Neural Networks · Physics 2011-11-10 T. I. Schelkacheva , N. M. Chtchelkatchev

It is well-known that the square principle $\square_\lambda$ entails the existence of a non-reflecting stationary subset of $\lambda^+$, whereas the weak square principle $\square^*_\lambda$ does not. Here we show that if…

Logic · Mathematics 2017-11-17 Gunter Fuchs , Assaf Rinot

We discuss stationary light created by a pair of counter-propagating control fields in Lambda-type atomic gases with electromagnetically induced transparency for the case of negligible Doppler broadening. In this case the secular…

Quantum Physics · Physics 2015-05-13 Gor Nikoghosyan , Michael Fleischhauer

We prove existence and uniqueness of L^p solutions of reflected backward stochastic differential equations with p-integrable data and generators satisfying the monotonicity condition. We also show that the solution may be approximated by…

Probability · Mathematics 2012-10-05 Andrzej Rozkosz , Leszek Slominski

If cf(kappa) = kappa, kappa^+< cf(lambda) = \lambda, then there is a stationary subset S of {delta<lambda:cf(delta)=kappa} in I[lambda]. Moreover, we can find <C_delta :delta in S>, C_delta a club of lambda, otp(C_delta)=kappa, guessing…

Logic · Mathematics 2008-06-03 Saharon Shelah

In this paper we continue the study in [Gilton-Levine-Stejskalova] of compactness and incompactness principles at double successors, focusing here on the case of double successors of singulars of countable cofinality. We obtain models which…

Logic · Mathematics 2024-08-13 Thomas Gilton , Šárka Stejskalová

We deal with the problem of preserving various versions of completeness in (< kappa) --support iterations of forcing notions, generalizing the case ``S --complete proper is preserved by CS iterations for a stationary co-stationary S…

Logic · Mathematics 2016-09-07 Saharon Shelah

In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2^omega = omega_2 and that…

Logic · Mathematics 2013-10-08 Justin Tatch Moore

We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal $\kappa \geq \omega$, there is a poset $\mathcal P_\kappa$ preserving all…

Logic · Mathematics 2015-07-16 Miguel Angel Mota , William Weiss

Saturation is (mu,kappa)-transferable in T if and only if there is an expansion T_1 of T with |T_1| = |T| such that if M is a mu-saturated model of T_1 and |M| \geq kappa then the reduct M|L(T) is kappa-saturated. We characterize theories…

Logic · Mathematics 2008-02-03 J. Baldwin , R. Grossberg , Saharon Shelah

We continue our study of maps transforming high-dimensional complicated objects into squares of stationary sets. Previously, we proved that many such transformations exist in ZFC, and here we address the consistency of the strongest…

Logic · Mathematics 2021-05-03 Assaf Rinot , Jing Zhang

Given any $\lambda\leq\kappa$, we construct a symmetric extension in which there is a set $X$ such that $\aleph(X)=\lambda$ and $\aleph^*(X)=\kappa$. Consequently, we show that $\mathsf{ZF}+$"For all pairs of infinite cardinals…

Logic · Mathematics 2024-08-16 Asaf Karagila , Calliope Ryan-Smith

We prove that for any $C^1$-stably weakly shadowing transitive set $\Lambda$, either $\Lambda$ is a sink or a source, or $\Lambda$ admits a dominated splitting.

Dynamical Systems · Mathematics 2010-03-11 Dawei Yang

In the present article we prove a fixed point theorem for reflections of compact convex sets and give a new characterization of state space of JB-algebras among compact convex sets. Namely they are exactly those compact convex sets which…

Functional Analysis · Mathematics 2011-10-04 Sh. A. Ayupov , N. J. Yadgorov

We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of…

Logic · Mathematics 2024-04-29 Tom Benhamou , Jing Zhang

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.

Representation Theory · Mathematics 2018-02-05 Kun Wang , Haitao Ma , Zhu-Jun Zheng

We give some general criteria, when kappa-complete forcing preserves largeness properties -- like kappa-presaturation of normal ideals on lambda (even when they concentrate on small cofinalities). Then we quite accurately obtain the…

Logic · Mathematics 2016-09-06 Moti Gitik , Saharon Shelah

Covering matrices were introduced by Viale in his proof that the Singular Cardinals Hypothesis follows from the Proper Forcing Axiom. In the course of his work and in subsequent work with Sharon, he isolated two reflection principles,…

Logic · Mathematics 2016-05-05 Chris Lambie-Hanson

A method is presented for modelling the optical properties of a photonic crystal structure mounted on a substrate which is thick enough that the light reflected from the back is incoherent with reflections from the front. Transmission and…

Optics · Physics 2010-12-17 D. M. Whittaker , G. A. Gehring

We study projective stationary sets. The Projective Stationary Reflection principle is the statement that every projective stationary set contains an increasing continuous $\in$--chain of length $\omega_1$. We show that if Martin's Maximum…

Logic · Mathematics 2009-09-25 Qi Feng , Thomas Jech