Iterated limits.

On Iterated Limits of Subsets of a Convergence -group

In this paper we deal with the relation lim α lim α X = lim α X for a subset X of G, where G is an -group and α is a sequential convergence on G.

Ratio limits and simulation algorithms for the Palm version of stationary iterated tessellations

Distributional properties and a simulation algorithm for the Palm version of stationary iterated tessellations are considered. In particular we study the limit behavior of functionals related to Cox-Voronoi cells (such as typical shortest path lengths) if either the intensity γ0 of the initial tessellation or the intensity γ1 of the component tessellation converges to 0. We develop an explicit ...

Iterated Local Reeection Vs Iterated Consistency

For \natural enough" systems of ordinal notation we show that times iterated local reeection schema over a suuciently strong arithmetic T proves the same 0 1-sentences as ! times iterated consistency. A corollary is that the two hierarchies catch up modulo relative interpretability exactly at-numbers. We also derive the following more general \mixed" formulas estimating the consistency strength...

Generalized Covering Groups and Direct Limits

Limits in modified categories of interest

‎We firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...