112,592 research outputs found
On the universal cover and the fundamental group of an -space
The main goal of the paper is to prove the existence of the universal cover
for -spaces. This generalizes earlier work of C. Sormani and the
second named author on the existence of universal covers for Ricci limit
spaces. As a result, we also obtain several structure results on the (revised)
fundamental group of such spaces. These are the first topological results for
-spaces without extra structural-topological assumptions (such as
semi-local simple connectedness).Comment: Final version to appear in Journal f\"ur die Reine und Angewandte
Mathemati
Galois-stability for Tame Abstract Elementary Classes
We introduce tame abstract elementary classes as a generalization of all
cases of abstract elementary classes that are known to permit development of
stability-like theory. In this paper we explore stability results in this
context. We assume that \K is a tame abstract elementary class satisfying the
amalgamation property with no maximal model. The main results include:
(1) Galois-stability above the Hanf number implies that \kappa(K) is less
than the Hanf number. Where \kappa(K) is the parallel of \kapppa(T) for f.o. T.
(2) We use (1) to construct Morley sequences (for non-splitting) improving
previous results of Shelah (from Sh394) and Grossberg & Lessmann.
(3) We obtain a partial stability-spectrum theorem for classes categorical
above the Hanf number.Comment: 23 page
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