Related papers: Ultrafilter extensions of linear orders
We define a special version of the ultralimit, called the skewed ultralimit. Using this tool, we show that the set of ultrafilter types in the $C$-equivalence class of a Ramsey ultrafilter $\mathfrak u\in \beta\omega$ with the Rudin-Keisler…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating…
Extensions (entropies) play a central role in the theory of hyperbolic conservation laws by providing intrinsic selection criteria for weak solutions. For a given hyperbolic system u_t+f(u)_x=0, a standard approach is to analyze directly…
We continue our study of the class $\mathscr{C}(D)$, where $D$ is a uniform ultrafilter on a cardinal $\kappa$ and $\mathscr{C}(D)$ is the class of all pairs $(\theta_1, \theta_2),$ where $(\theta_1, \theta_2)$ is the cofinality of a cut in…
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 develop the theory of residuated lattices by introducing and studying several new types of filters and related concepts, including semi-simple filters, essential filters, the socle of a filter, and independent families of filters. Our…
We consider the evaluation of first-order queries over classes of databases with bounded expansion. The notion of bounded expansion is fairly broad and generalizes bounded degree, bounded treewidth and exclusion of at least one minor. It…
Consider a population of heterogenous agents whose choice behaviors are partially \textit{comparable} according to a given \textit{primitive ordering}.The set of choice functions admissible in the population specifies a \textit{choice…
For a finite lattice $\Lambda$, $\Lambda$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $\Lambda$. This makes use of an isomorphism of…
Extensions of one-parameter operator semigroups on Archimedean vector lattices to their order/ru-completions are studied. Existence and uniqueness of the extension to the ru-completion is established in the class of positive semigroups. An…
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…
The underlying structure of natural language is hierarchical; words combine into phrases, which in turn form clauses. An awareness of this hierarchical structure can aid machine learning models in performing many linguistic tasks. However,…
We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the…
We study a new flexible method to extend linearly the graph of a non-linear, and usually not bijective, function so that the resulting extension is a bijection. Our motivation comes from cryptography. Examples from symmetric cryptography…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
A family of subsets $\mathcal{F} \subseteq \mathcal{P}(\{1, 2, \ldots, n\})$ has the disparate union property if any two disjoint subfamilies $\mathcal{F}_1, \mathcal{F}_2 \subseteq \mathcal{F}$ have distinct unions $\bigcup \mathcal{F}_1…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…