# Sh:377

- Shelah, S., Tuuri, H., & Väänänen, J. A. (1993).
*On the number of automorphisms of uncountable models*. J. Symbolic Logic,**58**(4), 1402–1418. arXiv: math/9301205 DOI: 10.2307/2275150 MR: 1253929 -
Abstract:

Let s({\mathcal A}) denote the number of automorphisms of a model {\mathcal A} of power \omega_1. We derive a necessary and sufficient condition in terms of trees for the existence of an {\mathcal A} with \omega_1 < s({\mathcal A}) < 2^{\omega_1}. We study the sufficiency of some conditions for s({\mathcal A})=2^{\omega_1}. These conditions are analogous to conditions studied by D.Kueker in connection with countable models. - published version (18p)

Bib entry

@article{Sh:377, author = {Shelah, Saharon and Tuuri, Heikki and V{\"a}{\"a}n{\"a}nen, Jouko A.}, title = {{On the number of automorphisms of uncountable models}}, journal = {J. Symbolic Logic}, fjournal = {The Journal of Symbolic Logic}, volume = {58}, number = {4}, year = {1993}, pages = {1402--1418}, issn = {0022-4812}, doi = {10.2307/2275150}, mrclass = {03C50}, mrnumber = {1253929}, mrreviewer = {Fuxing Shen}, doi = {10.2307/2275150}, note = {\href{https://arxiv.org/abs/math/9301205}{arXiv: math/9301205}}, arxiv_number = {math/9301205} }