Related papers: Ultrafilter extensions of linear orders
By using nonstandard analysis, and in particular iterated hyper-extensions, we give foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their pseudo-sums. The resulting formalism is suitable for…
The purpose of this paper is to investigate forcing as a tool to construct universal models. In particular, we look at theories of initial segments of the universe and show that any model of a sufficiently rich fragment of those theories…
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on…
Algebraic hyperstructures represent a natural extension of classical algebraic structures. In a classical algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two…
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under $G$ extends to a linear order on X also invariant under G. We…
Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large cardinals obtained that way (`Unfoldable cardinals') behave as…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
Given a semigroup $S$, we introduce relative (with respect to a filter $\tau$ on $S$) versions of large, thick and prethick subsets of $S$, give the ultrafilter characterizations of these subsets and explain how large could be some cell in…
Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…
In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
Neural language models trained with a predictive or masked objective have proven successful at capturing short and long distance syntactic dependencies. Here, we focus on verb argument structure in German, which has the interesting property…
We show that there exist models $\mathcal M_1$ and $\mathcal M_2$ such that $\mathcal M_1$ elementarily embeds into $\mathcal M_2$ but their ultrafilter extensions $\beta(\mathcal M_1)$ and $\beta(\mathcal M_2)$ are not elementarily…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
In this exposition, we get examples of what is called a "linear hyperdoctrine", based on categories of comodules indexed by coalgebras. This structures can model first order linear logic.
The ultrapower $T^{\ast}$ of an arbitrary ordered set $T$ is introduced as an infinitesimal extension of $T$. It is obtained as the set of equivalence classes of the sequences in $T$, where the corresponding relation is generated by an…
This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and…
We introduce the notion of extended affine Lie superalgebras and investigate the properties of their root systems. Extended affine Lie algebras, invariant affine reflection algebras, finite dimensional basic classical simple Lie…
We deal with first-order definability in the substructure ordering $(\mathcal{D}; \sqsubseteq)$ of finite directed graphs. In two papers, the author has already investigated the first-order language of the embeddability ordering $(…