Related papers: Ordinal ultrafilters versus P-hierarchy

Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We…

Interval graphs and interval orders are deeply linked. In fact, edges of an interval graphs represent the incomparability relation of an interval order, and in general, of different interval orders. The question about the conditions under…

In finite graphs, finite-order tangles offer an abstract description of highly connected substructures. In infinite graphs, infinite-order tangles compactify the graphs in the same way the ends compactify connected locally finite graphs.…

Caucal hierarchy is a well-known class of graphs with decidable monadic theories. It were proved by L. Braud and A. Carayol that well-orderings in the hierarchy are the well-orderings with order types less than $\varepsilon_0$. Naturally,…

We investigate families of partitions of omega which are related to special coideals, so-called happy families, and give a dual form of Ramsey ultrafilters in terms of partitions. The combinatorial properties of these…

There exist two distinct types of ultrafilter extensions of binary relations, one discovered in universal algebra and modal logic, and another, in model theory and algebra of ultrafilters. We show that the extension of the latter type is…

Assuming an abstract comparison principle called the Ultrapower Axiom, which is motivated by the comparison process of inner model theory and generalizes the statement that the Mitchell order is linear on normal ultrafilters, we…

This paper deals with variety of problems in pcf theory and infinitary combinatorics. We look at normal filters and prc, measures of the size of [lambda]^{<kappa}, pcf-inaccessibility, entangled orders (and narrow Boolean Algebras),…

Two-dimensional superintegrable systems with one third order and one lower order integral of motion are reviewed. The fact that Hamiltonian systems with higher order integrals of motion are not the same in classical and quantum mechanics is…

We extend some of our earlier results on the interconnection between ultrafilter extensions, and ultrapowers. Throughout we restrict ourselves to relational structures with one binary relation. Recently it was shown that for bounded…

In this paper, we introduce D-star order, T-star order and P-star order on the class of dual matrices. By applying matrix decomposition and dual generalized inverses, we discuss properties, characterizations and relations among these…

We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the…

Orbits of automorphism groups of partially ordered sets are not necessarily congruence classes, i.e. images of an order homomorphism. Based on so-called orbit categories a framework of factorisations and unfoldings is developed that…

In this paper we settle all questions whether (it is consistent that) the properties P and Q [do not] coincide, where P and Q run over selection principles of the type U_fin(O,A).

Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…

An assortments of `species' of families of subsets of a set and some of their properties are investigated, with an eye on the logic and limit role they may play as `relaxed parallels' to ultrafilters.

An ultrafilter $p$ on $\omega$ is said to be discrete if, given any function $f\colon \omega \to X$ to any completely regular Hausdorff space, there is an $A \in p$ such that $f(A)$ is discrete. Basic properties of discrete ultrafilters are…

We continue our investigation =of Shelah's interpretability orders $\trianglelefteq^*_\kappa$ as well as the new orders $\trianglelefteq^\times_\kappa$. In particular, we give streamlined proofs of the existence of minimal unstable,…

We use the Euler characteristic of the orbit category of a finite group to establish equivalences between theorems of Frobenius and K.S. Brown and between theorems of Steinberg and L. Solomon.

We find a strong separation between two natural families of simple rank one theories in Keisler's order: the theories $T_\mathfrak{m}$ reflecting graph sequences, which witness that Keisler's order has the maximum number of classes, and the…