Maximal failures of sequence locality in a.e.c

Details Maximal failures of sequence locality in a.e.c Maximal failures of sequence locality in a.e.c

2009-03-20

arxiv.org/abs/0903.3614v2

Mathematics

Logic

Scientific paper

We are interested in examples of a.e.c. with amalgamation having some (extreme) behaviour concerning types. Note we deal with k being sequence-local, i.e. local for increasing chains of length a regular cardinal. For any cardinal theta>= aleph_0 we construct an a.e.c. with amalgamation k with L.S.T.(k) = theta, |tau_K| = theta such that {kappa : kappa is a regular cardinal and K is not (2^kappa, kappa)-sequence-local} is maximal. In fact we have a direct characterization of this class of cardinals: the regular kappa such that there is no uniform kappa^+-complete ultrafilter. We also prove a similar result to "(2^kappa, kappa)-compact for types".

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