Sh:940

• Jarden, A., & Shelah, S. Non forking good frames minus local character. Preprint. arXiv: 1105.3674
• Abstract:
  We prove that if s is an almost good \lambda-frame (i.e. s is a good \lambda-frame except that it satisfies just a weak version of local character), then we can complete the frame s.t. it will satisfy local character too. This theorem has an important application. In [she46] it has proved that (under mild set theoretic assumptions) Categoricity in \lambda,\lambda^+ and intermediate number of models in K_{\lambda^{++}} implies existence of an almost good \lambda-frame. So by our theorem, we can get the local character too. So by categoricity assumptions in \lambda,\lambda^+, \lambda^{++} we can get existence of a good \lambda-frame. Combining this with [sh600], we conclude that the function \lambda \rightarrow I(\lambda,K), which correspond to each cardinal \lambda, the number of models in K of cardinality \lambda, is not arbitrary.
• Version 2010-09-14_11 (11p)

@article{Sh:940,
 author = {Jarden, Adi and Shelah, Saharon},
 title = {{Non forking good frames minus local character}},
 note = {\href{https://arxiv.org/abs/1105.3674}{arXiv: 1105.3674}},
 arxiv_number = {1105.3674}
}