Related papers: Effective Prime Uniqueness
With the increasing deployment of machine learning systems in practice, transparency and explainability have become serious issues. Contrastive explanations are considered to be useful and intuitive, in particular when it comes to…
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…
Given a represented space (in the sense of TTE theory), an appropriate representation is constructed for the Moschovakis extension of its carrier (with paying attention to the cases of effective topological spaces and effective metric…
Orbit-finite models of computation generalise the standard models of computation, to allow computation over infinite objects that are finite up to symmetries on atoms, denoted by $\mathbb{A}$. Set theory with atoms is used to reason about…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Effective and efficient forecasting relies on identification of the relevant information contained in past observations -- the predictive features -- and isolating it from the rest. When the future of a process bears a strong dependence on…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
We give a model-theoretic characterization of the class of geometric theories classified by an atomic topos having enough points; in particular, we show that every complete geometric theory classified by an atomic topos is countably…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
We introduce the definability strength of combinatorial principles. In terms of definability strength, a combinatorial principle is strong if solving a corresponding combinatorial problem could help in simplifying the definition of a…
We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.
We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several…
An effective quantum number determining with high accuracy the levels ordering in arbitrary centrally symmetric potentials for any space dimensionality is introduced and calculated by means of certain universal methods based on the known…
The separability tensor element of a separable extension of noncommutative rings is an idempotent when viewed in the correct endomorphism ring; so one speaks of a separability idempotent, as one usually does for separable algebras. It is…
Let $E$ be a $\mathbb Q$-curve without complex multiplication. We address the problem of deciding whether $E$ is geometrically isomorphic to a strongly modular $\mathbb Q$-curve. We show that the question has a positive answer if and only…
We show that a tensor product of irreducible, finite dimensional representations of a simple Lie algebra over a field of characteristic zero, determines the individual constituents uniquely. This is analogous to the uniqueness of prime…
We introduce a first-order theory of finite full binary trees and then identify decidable and undecidable fragments of this theory. We show that the analogue of Hilbert`s 10th Problem is undecidable by constructing a many-to-one reduction…
We consider the fragment F of first order arithmetic in which quantification is restricted to ''for all but finitely many.'' We show that the integers form an F-elementary substructure of the real numbers. Consequently, the F-theory of…
Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…
The main result of this paper is to show that all binomial identities are orderable. This is a natural statement in the combinatorial theory of finite sets, which can also be applied in distributed computing to derive new strong bounds on…