Related papers: Stable ordered-union versus selective ultrafilters
We present some new results on union ultrafilters. We characterize stability for union ultrafilters and, as the main result, we construct a new kind of unordered union ultrafilter.
A union ultrafilter is an ultrafilter over the finite subsets of $\omega$ that has a base of sets of the form $\mathrm{FU}(X)$, where $X$ is an infinite pairwise disjoint family and $\mathrm{FU}(X)=\{\bigcup…
We survey some recent results about the order structure of various kinds of ultrafilters. More precisely, we study Rudin-Keisler and Tukey reducibility in classes of selective, stable ordered-union, and P-point ultrafilters. Although these…
We study some limitations and possible occurrences of uniform ultrafilters on ordinals without the axiom of choice. We prove an Easton-like theorem about the possible spectrum of successors of regular cardinals which carry uniform…
In the first edition of Classification Theory, the second author characterized the stable theories in terms of saturation of ultrapowers. Prior to this theorem, stability had already been defined in terms of counting types, and the unstable…
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability.…
A stable filter has the property that it asymptotically `forgets' initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words…
Despite being a foundational concept of modern systems theory, there have been few studies on observability of non-linear stochastic systems under partial observations. In this paper, we introduce a definition of observability for…
We characterize ultrafilter convergence and ultrafilter compactness in linearly ordered and generalized ordered topological spaces. In such spaces, and for every ultrafilter $D$, the notions of $D$-compactness and of $D$-pseudocompactness…
In \cite{HK}, Hayut and Karagila asked some questions about uniform ultrafilters in a choiceless context. We provide several answers to their questions.
This paper examines the stability of the \`a trous algorithm under arbitrary iteration in the context of a more general study of shift-invariant filter banks. The main results describe sufficient conditions on the associated filters under…
It is proved to be consistent relative to a measurable cardinal that there is a uniform ultrafilter on the real numbers which is generated by fewer than the maximum possible number of sets. It is also shown to be consistent relative to a…
We discuss the connection between various orders on the class of all the ultrafilters and certain compactness properties of abstract logics and of topological spaces. We present a model theoretical characterization of Comfort order. We…
A hidden Markov model is called observable if distinct initial laws give rise to distinct laws of the observation process. Observability implies stability of the nonlinear filter when the signal process is tight, but this need not be the…
We answer two questions of Hindman, Stepr\=ans and Strauss, namely we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover we show that in most cases the sparseness of the…
We study a uniform version of the strong diameter two property. In particular, we find a characterisation that does not involve ultrafilters and we use it to provide some examples of spaces with this uniform property that do not follow from…
An ultrafilter U is Hausdorff if for any two functions f,g mapping N to N, f(U)=g(U) iff f(n)=g(n) for n in some X in U. We will show that it is consistent that there are no Hausdorff ultrafilters.
Due to the lack of long-range order, it remains challenging to characterize the structure of disordered solids and understand the nature of the glass transition. Here we propose a new structural order parameter by taking into account…
In this paper we analyse and compare two different notions of regularity for filters on complete Boolean algebras. We also announce two results from a forthcoming paper in preparation, which provide a characterization of Keisler's order in…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…