# Sh:1042

- Farah, I., & Shelah, S. (2016).
*Rigidity of continuous quotients*. J. Inst. Math. Jussieu,**15**(1), 1–28. arXiv: 1401.6689 DOI: 10.1017/S1474748014000218 MR: 3427592 -
Abstract:

The assertion that the Čech–Stone remainder of the half-line has only trivial automorphisms is independent from ZFC. The consistency of this statement follows from Proper Forcing Axiom and this is the first known example of a connected space with this property. The existence of 2^{\aleph_1} autohomeomorphisms under the Continuum Hypothesis follows from a general model-theoretic fact. We introduce continuous fields of metric models and prove countable saturation of the corresponding reduced products. We also provide an (overdue) proof that the reduced products of metric models corresponding to the Fréchet ideal are countably saturated. This provides an explanation of why the asymptotic sequence C*- algebras and the central sequence C*-algebras are as useful as ultrapowers. - published version (28p)

Bib entry

@article{Sh:1042, author = {Farah, Ilijas and Shelah, Saharon}, title = {{Rigidity of continuous quotients}}, journal = {J. Inst. Math. Jussieu}, fjournal = {Journal of the Institute of Mathematics of Jussieu. JIMJ. Journal de l'Institut de Math\'ematiques de Jussieu}, volume = {15}, number = {1}, year = {2016}, pages = {1--28}, issn = {1474-7480}, doi = {10.1017/S1474748014000218}, mrclass = {03C65 (03E35 03E50 03E57 46L05)}, mrnumber = {3427592}, mrreviewer = {Camilo Enrique Argoty}, doi = {10.1017/S1474748014000218}, note = {\href{https://arxiv.org/abs/1401.6689}{arXiv: 1401.6689}}, arxiv_number = {1401.6689} }