We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural " tangent 2-bundle, " analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relati...

We introduce various probabilistic finiteness conditions for profinite groups related to positive finite generation (PFG). investigate completed group rings which are PFG as modules, and use this answer [17, Question 1.2] on positively finitely groups. Using the theory of projective covers, we define characterise a version FPn property groups, called PFPn. Finally, prove how these previously de...

certain algebraic invariants of the integral group ring zg of a group g were introduced and investigated in relation to the problem of extending the farrell-tate cohomology, which is defined for the class of groups of finite virtual cohomological dimension. it turns out that the finiteness of these invariants of a group g implies the existence of a generalized farrell-tate cohomology for g whic...

We investigate a new denotational model of linear logic based on the purely relational model. In this semantics, webs are equipped with a notion of “finitary” subsets satisfying a closure condition and proofs are interpreted as finitary sets. In spite of a formal similarity, this model is quite different from the usual models of linear logic (coherence semantics, hypercoherence semantics, the v...

In this paper we solve the satisfiability problem for a quantifier-free fragment of set theory involving the powerset and the singleton operators and a finiteness predicate, besides the basic Boolean set operators of union, intersection, and difference. The more restricted fragment obtained by dropping the finiteness predicate has been shown to have a solvable satisfiability problem in a previo...

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V . In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of Swiss-cheese partial operad. We also give a tensor-categorical formulation and constructions of open-c...

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural " tangent 2-bundle, " analogous to the tangent bundle of a smooth manifold. Examples with reasonable finiteness conditions have an intrinsic geometry, which can approximate classical solutions to general relati...

We calculate the two-loop β-functions for soft supersymmetry-breaking interactions in a general supersymmetric gauge theory, emphasising the role of the evanescent couplings and masses that are generic to a non-supersymmetric theory. We also show that a simple set of conditions sufficient for one-loop finiteness renders a theory two-loop finite, and we speculate on the possible significance of ...

We consider the class of all commutative reduced rings for which there exists a finite subset T ⊂ A such that all projections on quotients by prime ideals of A are surjective when restricted to T . A complete structure theorem is given for this class of rings, and it is studied its relation with other finiteness conditions on the quotients of a ring over its prime ideals. Introduction Our aim i...