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We show how to decompose all separable ultrametric spaces into a "Lego" combinations of scaled versions of full simplices. To do this we introduce metric resolutions of large scale metric spaces, which describe how a space can be broken up…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
A first-order theory $T$ is a model-complete core theory if every first-order formula is equivalent modulo $T$ to an existential positive formula; the core companion of a theory $T$ is a model-complete core theory $S$ such that every model…
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…
Merging has become a widespread way to cheaply combine individual models into a single model that inherits their capabilities and attains better performance. This popularity has spurred rapid development of many new merging methods, which…
Our aim is to solve a quite old question on the difference between expandability and compact expandability. Toward this, we further investigate the logic of countable cofinality.
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
This paper shows how internal models for polymorphic lambda calculi arise in any 2-category with a notion of discreteness. We generalise to a 2-categorical setting the famous theorem of Peter Freyd saying that there are no sufficiently…
This paper studies Moore's measurable cohomology theory for locally compact groups and Polish modules. An elementary dimension-shifting argument is used to show that all classes in that theory have representatives with considerable extra…
We extend the recently introduced setting of coherent differentiation for taking into account not only differentiation, but also Taylor expansion in categories which are not necessarily (left)additive. The main idea consists in extending…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
In this paper we generalise the notion of linearity (in the sense of Lawvere) to a category C equipped with a compatible sum structure and product structure. In this context, any morphism f from an n-fold sum to an n-fold product has a…
Computability theory is traditionally conceived as the theoretical basis of informatics. Nevertheless, numerous proposals transcend computability theory, in particular by emphasizing interaction of modules, or components, parts,…
A mechanical linkage is a mechanism made of rigid rods linked together by flexible joints, in which some vertices are fixed and others may move. The partial configuration space of a linkage is the set of all the possible positions of a…
Working in any model theoretic structure, we single out a class of definable bipartite graphs that admit definable, close to perfect matchings. We use this result to prove a strengthening of Tarski's theorem for the definable setting.
We propose a generalization of first-order logic originating in a neglected work by C.C. Chang: a natural and generic correspondence language for any types of structures which can be recast as Set-coalgebras. We discuss axiomatization and…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous…
An appeal for symmetry is made to build established notions of specific representation and specific nonlinearity of measurement (often called model error) into a canonical linear regression model. Additive components are derived from the…