相关论文: Dynamical ideals and the axiom of choice

A recent paper by Zapletal arXiv:2404.10612 discusses permutation models of set theory which arise from dynamical ideals and highlights properties of the dynamical ideal which relate to fragments of choice in the permutation model. In this…

We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.

We introduce and prove the consistency of a new set theoretic axiom we call the \emph{Invariant Ideal Axiom}. The axiom enables us to provide (consistently) a full topological classification of countable sequential groups, as well as fully…

This article offers a gentle introduction to the axiom of choice. We introduce the axiom, discuss some common objections to it, and present three kinds of reasons to accept it. Although the exposition is aimed at non-experts in set theory,…

It is shown, from $\sigma$-centered Martin's Axiom, that there exists a proper dense subgroup of the symmetric group on a countably infinite set whose natural action on sufficiently flexible relational structures is transitive. This allows…

People care about decision outcomes and how decisions get made, both when making decisions and reflecting on decisions. But formalizing the full range of normative concerns that drive decisions is an open challenge. We introduce Axiomatic…

The formation mechanisms and cyclical conditions of collective action have become open issues in research involving public choice, social movements, and more. For this reason, on the basis of rational decision-making and social…

Some basic notions and results in Topological Dynamics are extended to continuous groupoid actions in topological spaces. We focus mainly on recurrence properties. Besides results that are analogous to the classical case of group actions,…

Consideration of certain properties of group rings and their ideals search

We review novel results and investigate actions and transformations of groups and semigroups on (quantum) spaces, present dynamical systems and zeta functions arising from these spaces, actions and transformations, discuss their stochastic…

In this paper we present a new characterization of free group actions (in classical differential geometry), involving dynamical systems and representations of the corresponding transformation groups. In fact, given a dynamical system, we…

A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional…

This article introduces patterns of ideals of numerical semigroups, thereby unifying previous definitions of patterns of numerical semigroups. Several results of general interest are proved. More precisely, this article presents results on…

Emergent collective group processes and capabilities have been studied through analysis of transactive memory, measures of group task performance, and group intelligence, among others. In their approach to collective behaviors, these…

We construct a commutative version of the group ring and show that it allows one to translate questions about the normal generation of groups into questions about the generation of ideals in commutative rings. We demonstrate this with an…

After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…

We study a class of determinantal ideals that are related to conditional independence (CI) statements with hidden variables. Such CI statements correspond to determinantal conditions on a matrix whose entries are probabilities of events…

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…

We propose a dynamical model for group formation and switching behavior in systems where each group competes for members through attraction functions that are inversely proportional to their current sizes. This attraction is modulated by…

This article analyses the properties of the Internal Behaviour network, an action selection mechanism previously proposed by the authors, with the aid of a simulation developed for such ends. A brief review of the Internal Behaviour network…