相关论文: Ind- and Pro- definable sets
We characterize those intersection-type theories which yield complete intersection-type assignment systems for lambda-calculi, with respect to the three canonical set-theoretical semantics for intersection-types: the inference semantics,…
We define and study a higher-dimensional version of model theoretic internality, and relate it to higher-dimensional definable groupoids in the base theory.
We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.
We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound of definable countable ordinals in the Zermelo-Fraenkel's set theory ZF.
In this paper we provide a semantic and syntactic analysis of parametrised natural numbers object in coherent categories, or pr-coherent categories. Semantically, we show the definable functions in the initial pr-coherent category are…
Category theory provides a powerful tool to organize mathematics. A sample of this descriptive power is given by the categorical analysis of the practice of "classes as shorthands" in ZF set theory. In this case category theory provides a…
As the prototypical category, $\mathbf{Set}$ has many properties which make it special amongst categories. From the point of view of mathematical logic, one such property is that $\mathbf{Set}$ has enough structure to "properly" formalise…
Classification theory of elementary classes deals with first order (elementary) classes of structures (i.e. fixing a set T of first order sentences, we investigate the class of models of T with the elementary submodel notion). It tries to…
We study semantic and syntactic properties of spherical orders and their elementary theories, including finite and dense orders and their theories. It is shown that theories of dense $n$-spherical orders are countably categorical and…
The set of integer number lists with finite length, and the set of binary trees with integer labels are both countably infinite. Many inductively defined types also have countably many elements. In this paper, we formalize the syntax of…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
In this note we introduce and characterize a class of finite groups for which the element orders satisfy a certain inequality. This is contained in some well-known classes of finite groups.
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
We define a monoidal semantics for algebraic theories. The basis for the definition is provided by the analysis of the structural rules in the term calculus of algebraic languages. Models are described both explicitly, in a form that…
We introduce enriched notions of purity depending on the left class $\mathcal E$ of a factorization system on the base $\mathcal V$ of enrichment. Ordinary purity is given by the class of surjective mappings in the category of sets. Under…
We develop some aspects of the model theory of additive structures, with particular emphasis on the abelian category of pp-imaginaries.
In this paper we study grouplike monoids, these are monoids that contain a group to which we add an ordered set of idempotents. We classify finite categories with two objects having grouplike endomorphism monoids, and we give a count of…
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting…
Commensurable groups are bi-interpretable, under suitable definability conditions.
Definable topological groups whose topologies are affine have definable $\mathcal C^r$ structures in d-minimal expansions of ordered fields, where $r$ is a positive integer. We prove this fact using a new notion called partition degree of a…