# Sh:664

- Shelah, S. (2001).
*Strong dichotomy of cardinality*. Results Math.,**39**(1-2), 131–154. arXiv: math/9807183 DOI: 10.1007/BF03322680 MR: 1817405 -
Abstract:

A usual dichotomy is that in many cases, reasonably definable sets, satisfy the CH, i.e. if they are uncountable they have cardinality continuum. A strong dichotomy is when: if the cardinality is infinite it is continuum as in [Sh:273]. We are interested in such phenomena when \lambda=\aleph_0 is replaced by \lambda regular uncountable and also by \lambda=\beth_\omega or more generally by strong limit of cofinality \aleph_0. - published version (24p)

Bib entry

@article{Sh:664, author = {Shelah, Saharon}, title = {{Strong dichotomy of cardinality}}, journal = {Results Math.}, fjournal = {Results in Mathematics. Resultate der Mathematik}, volume = {39}, number = {1-2}, year = {2001}, pages = {131--154}, issn = {0378-6218}, mrnumber = {1817405}, mrclass = {03E99 (03E15 20K99)}, doi = {10.1007/BF03322680}, note = {\href{https://arxiv.org/abs/math/9807183}{arXiv: math/9807183}}, arxiv_number = {math/9807183} }