Related papers: A class of fields with a restricted model complete…
We present the model theoretic concepts that allow mathematics to be developed with the notion of the potential infinite instead of the actual infinite. The potential infinite is understood as a dynamic notion, being an indefinitely…
We study a class of scalar field models coupled to impurities in arbitrary spacetime dimensions. The system admits the introduction of a second-order tensor that can be forced to obey an equality, if a first-order differential equation is…
We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a given bound.
We study existential theories of henselian valued fields of positive characteristic with parameters from a trivially valued subfield. Compared to previous work, we relax perfectness and separability assumptions, and instead work with the…
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…
The monadic second-order theory of trees allows quantification over elements and over arbitrary subsets. We classify the class of trees with respect to the question: does a tree T have a definable choice function (by a monadic formula with…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
We prove that the (elementary) class of differential-difference fields in characteristic $p>0$ admits a model-companion. In the terminology of Chatzidakis-Pillay, this says that the class of differentially closed fields of characteristic…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
A modeling formalism is proposed for the description and study of living and life-like systems. It provides an abstract conceptual model framework for real life and evolution of biological organisms. It is proposed, that this model…
We provide a characterization of almost ordinary abelian varieties over finite fields, and use this characterization to provide lower bounds for the sizes of some almost ordinary isogeny classes.
In this article, we focus on orders in arbitrary number fields, consider their Picard groups and finally obtain ring class fields corresponding to them. The Galois group of the ring class field is isomorphic to the Picard group. As an…
We construct small models of number fields and deduce a better bound for the number of number fields of given degree and bounded discriminant.
We define general notions of coordinate geometries over fields and ordered fields, and consider coordinate geometries that are given by finitely many relations that are definable over those fields. We show that the automorphism group of…
We construct compact descriptions of function fields and number fields.
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the…
Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions…
For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…
Tree sets are abstract structures that can be used to model various tree-shaped objects in combinatorics. Finite tree sets can be represented by finite graph-theoretical trees. We extend this representation theory to infinite tree sets.…