Related papers: Sticks and clubs
We explore new interactions between finite model theory and classical streams of universal algebra and semigroup theory. A key result is an example of finite algebras whose variety is not finitely axiomatisable in first order logic, but…
A novel selection principle was introduced by Dorantes-Aldama and Shakhmatov: a topological space $X$ is termed {\em selectively pseudocompact} if for any sequence $(U_n:n\in {\omega})$ of pairwise disjoint non-empty open sets of $X$, one…
An abstract sampling theory associated to a unitary representation of a countable discrete non abelian group $G$, which is a semi-direct product of groups, on a separable Hilbert space is studied. A suitable expression of the data samples…
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
We consider stable and semistable principal bundles over a smooth projective real algebraic curve, equipped with a real or pseudo-real structure in the sense of Atiyah. After fixing suitable topological invariants, one can build a suitable…
This is an attempt to model ambient space as a three-dimensional real affine space with a distinguished group of automorphisms containing the translations and acting freely and transitively on pairs consisting of a half-plane together with…
We discuss how singular can cardinals be in absence of the axiom of choice. We show that, contrasting with known negative consistency results (of Gitik and others), certain positive results are provable. Then we pose some problems.
We analyze combinatorial optimization problems over a pair of random point sets of equal cardinal. Typical examples include the matching of minimal length, the traveling salesperson tour constrained to alternate between points of each set,…
We consider a semi-classical approximation to the dynamics of a point particle in a noncommutative space. In this approximation, the noncommutativity of space coordinates is described by a Poisson bracket. For linear Poisson brackets, the…
We consider positively supported Borel measures for which all moments exist. On the set of compactly supported measures in this class a partial order is defined via eventual dominance of the moment sequences. Special classes are identified…
We define a weak iterability notion that is sufficient for a number of arguments concerning $\Sigma_1$-definability at uncountable regular cardinals. In particular we give its exact consistency strength firstly in terms of the second…
A permutoid is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that…
We pursue the question how integers can be ordered or partitioned according to their divisibility properties. Based on pseudometrics on $\mathbb{Z}$, we investigate induced preorders, associated equivalence relations, and quotient sets. The…
For a finite dimensional spin-glass model we prove local order at low temperatures for both local observables and for products of observables at arbitrary mutual distance. When the Hamiltonian includes the Edwards-Anderson interaction we…
We present a new notion of non-positively curved groups: the collection of discrete countable groups acting (AU-)acylindrically on finite products of $\delta$-hyperbolic spaces with general type factors and associated subdirect products.…
We study the Stable Fixtures problem, a many-to-many generalisation of the classical non-bipartite Stable Roommates matching problem. Building on the foundational work of Tan on stable partitions, we extend his results to this significantly…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
The choice of a star product realization for noncommutative field theory can be regarded as a gauge choice in the space of all equivalent star products. With the goal of having a gauge invariant treatment, we develop tools, such as…
We study first-order concatenation theory with bounded quantifiers. We give axiomatizations with interesting properties, and we prove some normal-form results. Finally, we prove a number of decidability and undecidability results.
I prove two variants of the $ABC$ sum-product theorem for $\delta$-separated sets $A,B,C \subset [0,1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality of the sets $B,C$ need not match their…