This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from Coh to Fin commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiten...

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications the main results include characterization what finitely presentable groups may admit into hyperbolic group geometric dimension 2, characterizations subgroups with quadratic function and to embeddings nilpotent other same growth groups.

In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. We extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions, using nonstabilized normal bordism theory as our main tool. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coinciden...

We prove that the Farrell-Jones assembly map for connective algebraic K-theory is rationally injective, under mild homological finiteness conditions on the group and assuming that a weak version of the Leopoldt-Schneider conjecture holds for cyclotomic fields. This generalizes a result of Bökstedt, Hsiang, and Madsen, and leads to a concrete description of a large direct summand of Kn(Z[G])⊗Z Q...

Perhaps the most fundamental problem in the theory of natural dualities is the dualisability problem: deciding exactly which finite algebras generate a quasivariety that admits a natural duality. One of the goals of this paper is to demonstrate the difficulty of this problem. To do this, we solve the dualisability problem restricted to a class of apparently very simple algebras: three-element u...

The joint spectral radius of a finite set of real d × d matrices is defined to be the maximum possible exponential rate of growth of long products of matrices drawn from that set. A set of matrices is said to have the finiteness property if there exists a periodic product which achieves this maximal rate of growth. J. C. Lagarias and Y. Wang conjectured in 1995 that every finite set of real d× ...

I will discuss some aspects of the treatment of finiteness in its various facets given in (1) in the nontransformational theories of Head-Driven Phrase Structure Grammar (HPSG) and Lexical-Functional Grammar (LFG).1 Due to the way that syntactic information is represented in these approaches, it can be stated at the outset that finiteness is considered to really be a property of a clause. From ...

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under Frobenius twist for Ext-groups.

In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+ that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusion...

For the multivariate COGARCH(1,1) volatility process we show sufficient conditions for the existence of a unique stationary distribution, for the geometric ergodicity and for the finiteness of moments of the stationary distribution. One of the conditions demands a sufficiently fast exponential decay of the MUCOGARCH(1,1) volatility process. Furthermore, we show easily applicable sufficient cond...