We give a general structure theory for reconstructing group actions on sets without any assumptions on the group, the action, or the set on which the group acts. Using certain ‘local data’ D from the action we build a group G(D) of the data and a space X (D) with an action of G(D) on X (D) that arise naturally from the data D. We use these to obtain an approximation to the original group G, the...

In this paper, we introduce a logic to reason about group actions for groups that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The logic of action that we use here for modelling group actions is based on a substructural propositional logic that allows f...

Let G be a simple primitive subgroup of Sn, speciied in terms of a set of generating permutations. If jGj n 5 , eecient algorithms are presented that nd \the most natural permutation representation" of G. For example, if G is a classical group then we nd a suitable projective space underlying G. A number of related questions are considered. Our notion of \eeciency" takes into account many exist...

This paper deals with measurable stationary symmetric stable random fields indexed by R and their relationship with the ergodic theory of nonsingular R-actions. Based on the phenomenal work of Rosiński (2000), we establish extensions of some structure results of stationary SαS processes to SαS fields. Depending on the ergodic theoretical nature of the underlying action, we observe different beh...

Let G be a noncompact real algebraic group and Γ < G a lattice. One purpose of this paper is to show that there is an smooth, volume preserving, mixing action of G or Γ on a compact manifold which admits a smooth deformation. We also describe some other, rather special, deformations when G = SO(1, n) and provide a simple proof that any action of a compact Lie group is locally rigid.

Using methods from computable analysis, we establish a new connection between two seemingly distant areas of logic: computable structure theory and invariant descriptive set theory. We extend several fundamental results of computable structure theory to the more general setting of topological group actions. Among other results, we provide a new recursion-theoretic characterization of Σ3-orbits ...

In this paper we study quotients of posets by group actions. In order to define the quotient correctly we enlarge the considered class of categories from posets to loopfree categories: categories without nontrivial automorphisms and inverses. We view group actions as certain functors and define the quotients as colimits of these functors. The advantage of this definition over studying the quoti...

For this paper, we will define a (non-oriented) graph Γ to be a pair Γ = (V,E), where V = vert(Γ) is a set of vertices, and E = edge(Γ) ⊆ V × V/S2 is a set of unordered pairs, known as edges between them. Two vertices, v, v′ ∈ V are considered adjacent if (v, v′) ∈ E, if there is an edge between them. An oriented graph has edge set E = edge(Γ) ⊆ V × V , ordered pairs. For an edge v = (v1, v2) i...