• Corpus ID: 15822902

Maximal failures of sequence locality in a.e.c

@article{Shelah2009MaximalFO,
  title={Maximal failures of sequence locality in a.e.c},
  author={Saharon Shelah},
  journal={arXiv: Logic},
  year={2009}
}

• S. Shelah
• Published 20 March 2009
• Mathematics, Biology
• arXiv: Logic

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 types, equality of all restrictions imply equality). . 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".