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1. The Lattice of Definability: Origins, Recent Developments, and Further Directions

   Abstract

   This article presents results and open problems related to definability spaces (reducts) and sources of this field since the 19th century....

   A. L. Semenov, S. F. Soprunov in Doklady Mathematics

   Article 01 December 2022

2. Modal Definability: Two Commuting Equivalence Relations

   We prove that modal definability with respect to the class of all structures with two commuting equivalence relations is an undecidable problem. The...

   Yana Rumenova, Tinko Tinchev in Logica Universalis

   Article 08 February 2022
   

3. On relatively elementary definability of graph classes in the class of semigroups

   Based on the previously obtained concrete characterization of the endomorphism semigroups of quasi-acyclic reflexive graphs we prove the relatively...

   Vladimir A. Molchanov in Algebra universalis

   Article 27 June 2022

4. Relatively Elementary Definability of the Class of Universal Graphic Semiautomata in the Class of Semigroups

   Abstract

   Automata theory is a branch of mathematical cybernetics that studies data conversion devices involved in many applied problems. This article...

   R. A. Farakhutdinov in Russian Mathematics

   Article 01 January 2022

5. Definability of Relations by Semigroups of Isotone Transformations

   A. A. Klyushin, I. B. Kozhukhov, ... A. V. Reshetnikov in Journal of Applied and Industrial Mathematics

   Article 01 March 2024

6. Existential Definability of Unary Predicates in Büchi Arithmetic

   The paper provides a complete characterisation of the sets $$S\subseteq \mathbb...

   Mikhail R. Starchak in Twenty Years of Theoretical and Practical Synergies

   Conference paper 2024
   

7. Minimal Predicates for Δ-Definability

   We consider two kinds of reducibilities on finite families of predicates on a countable set: the definability of predicates and their complements of...

   A. S. Morozov, D. A. Tussupov in Algebra and Logic

   Article 01 September 2020

8. Definability in the Substructure Ordering of Finite Directed Graphs

   Ádám Kunos in Order

   Article 23 January 2021

9. Lattice of Definability in the Order of Rational Numbers

   Abstract

   A lattice of definability subspaces in the order of rational numbers is described. It is proved that this lattice consists of five subspaces...

   An. A. Muchnik, A. L. Semenov in Mathematical Notes

   Article 01 July 2020
   

10. Creating New Mathematics by Schoolchildren

    Abstract

    The paper discusses an example of an educational project in modern mathematics in which school students create mathematics that is new to...

    A. L. Semenov, S. F. Soprunov, I. A. Ivanov-Pogodaev in Doklady Mathematics

    Article Open access 01 July 2023

11. On Σ-Definability Over Hereditarily Finite and List Superstructures

    We establish the reciprocal Σ-definability of the hereditarily finite superstructure and the hereditarily finite list superstructure over an...

    S. A. Aleksandrova in Journal of Mathematical Sciences

    Article 11 April 2020

12. Between the Rings \({\mathbb Z}/p^n{\mathbb Z}\) and the Ring \({\mathbb Z}_p\) : Issues of Axiomatizability, Definability and Decidability

    Angus J. Macintyre in Mathematics Going Forward

    Chapter 2023
    

13. Definability of Completely Decomposable Torsion-Free Abelian Groups by Semigroups of Endomorphisms and Groups of Homomorphisms

    Let C be an Abelian group. A class X of Abelian groups is called a _C E ^• H -class if for any groups A, B ∈ X , it follows from the existence of...

    T. A. Pushkova in Journal of Mathematical Sciences

    Article 08 November 2021

14. The automorphism group and definability of the jump operator in the \(\omega \)-enumeration degrees

    Hristo Ganchev, Andrey C. Sariev in Archive for Mathematical Logic

    Article 01 April 2021

15. Semigroups of Relatively Continuous Binary Relations and Their Isomorphisms

    Abstract

    All isomorphisms between semigroups of relatively continuous binary relations defined on arbitrary topological spaces are described. As a...

    V. I. Varankina, E. M. Vechtomov in Mathematical Notes

    Article 20 June 2023

16. On Mutual Definability of Operations on Fields

    We study the possibilities of defining some operations on fields via the remaining operations. In particular, we prove that multiplication on an...

    R. M. Korotkova, O. V. Kudinov, A. S. Morozov in Siberian Mathematical Journal

    Article 01 November 2019

17. On the Question of the Definability of Certain Classes of Completely Decomposable Abelian Torsion-Free Groups by Their Homomorphism Groups

    T. A. Pushkova, A. M. Sebel’din in Mathematical Notes

    Article 20 June 2023

18. Ultravaluations and their Applications in \(\textsf{CPL}\)

    This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this...

    Krzysztof A. Krawczyk, Bożena Piȩta in Logica Universalis

    Article Open access 16 June 2023

19. Conservative Parametric Optimality and the Ridge Method for Tame Min-Max Problems

    We study the ridge method for min-max problems, and investigate its convergence without any convexity, differentiability or qualification assumption....

    Edouard Pauwels in Set-Valued and Variational Analysis

    Article 22 June 2023

20. The Relationship Between Local and Global Structure in the Enumeration Degrees

    We discuss core ideas in degree theory including biinterpretability, automorphisms, and definability. We focus on the Turing degrees...

    Mariya I. Soskova in Unity of Logic and Computation

    Conference paper 2023