Related papers: Sacks Forcing and the Shrink Wrapping Property
By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its…
It is shown how to construct, given a Banach space which does not have the approximation property, another Banach space which does not have the approximation property but which does have the compact approximation property.
We construct a model in which the tree property holds in $\aleph_{\omega + 1}$ and it is destructible under $\text{Col}(\omega, \omega_1)$. On the other hand we discuss some cases in which the tree property is indestructible under small or…
A countable structure is said to be extendible if it has the same Scott sentence as some uncountable structure. Rigid structures are not extendible. We give an example of an extendible model with a rigid elementary extension.
A tournament is said to have the $S_k$-property if, for any set of $k$ players, there is another player who beats them all. Minimum tournaments having this property have been explored very well in the 1960's and the early 1970's. In this…
For a slim, planar, semimodular lattice, G. Cz\'edli and E.\,T. Schmidt introduced the fork extension in 2012. In this note we prove that the fork extension has the Congruence Extension Property. This paper has been merged with Part II,…
We use the local load sharing fiber bundle model to demonstrate a shielding effect where strong fibers protect weaker ones. This effect exists due to the local stress enhancement around broken fibers in the local load sharing model, and it…
We demonstrate that there is a large class of compact metric spaces for which the shadowing property can be characterized as a structural property of the space of dynamical systems. We also demonstrate for this class of spaces, that in…
In this paper we answer several questions in arXiv:2102.06009 regarding density variants of Mathias and Silver forcing. These questions include whether each of the forcing is proper, add dominating real, or add Cohen real. We also…
We show that many countable support iterations of proper forcings preserve Souslin trees. We establish sufficient conditions in terms of games and we draw connections to other preservation properties. We present a proof of preservation…
We address the important question of the extent to which random variables and vectors with truncated power tails retain the characteristic features of random variables and vectors with power tails. We define two truncation regimes, soft…
Trading a financial instrument pushes its price and those of other assets, a phenomenon known as cross-impact. To be of use, cross-impact models must fit data and be well-behaved so they can be applied in applications such as optimal…
Weak mixing in lattice models is informally the property that ``information does not propagate inside a system''. Strong mixing is the property that ``information does not propagate inside and on the boundary of a system''. In dimension…
For a quasimartingale majorized by another quasimartingale, it is natural to ask whether a third quasimartingale can be inserted between them. In this paper, we give an affirmative answer to this problem. We also establish a dominated…
We observe that justification logic enjoys a form the strong finite model property (sometimes also called small model property). Thus we obtain decidability proofs for justification logic that do not rely on Post's theorem.
Recently, two stronger versions of dynamical properties have been introduced and investigated: strong topological transitivity, which is a stronger version of the topological transitivity property, and hypermixing, which is a stronger…
Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition…
We prove that in the Miller model the Menger property is preserved by finite products of metrizable spaces. This answers several open questions and gives another instance of the interplay between classical forcing posets with fusion and…
We give a short review of a construction of Frink to obtain a metric space from a quasi-metric space. By an example we illustrate the limits of the construction.
In the first part of the paper, we show that if $\omega \le \kappa < \lambda$ are cardinals, $\kappa^{<\kappa} = \kappa$, and $\lambda$ is weakly compact, then in $V[\M(\kappa,\lambda)]$ the tree property at $\lambda =…