Canonical universal locally finite groups
Rendiconti del Seminario Matematico della Università di Padova, Tome 149 (2023), pp. 25-44.
Le texte intégral des articles récents est réservé aux abonnés de la revue. Consultez l'article sur le site de la revue.

We prove that the existence of universally locally finite groups implies that there is a canonical one in any strong limit singular cardinality of countable cofinality. Moreover, those canonical groups are parallel to the special models for complete first order theories. For showing the existence we rely on the existence of enough indecomposable such groups as we proved in [Rend. Sem. Mat. Univ. Padova 144 (2020), 253–270]. More generally, we also deal with the existence of a universal member in general classes for such cardinals.

Publié le :
DOI : 10.4171/rsmup/117
Classification : 20, 03 
@article{RSMUP_2023__149__25_0,
     author = {Saharon Shelah},
     title = {Canonical universal locally finite groups},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {25--44},
     volume = {149},
     year = {2023},
     doi = {10.4171/rsmup/117},
     mrnumber = {4575363},
     zbl = {07688316},
     language = {en},
     url = {http://archive.numdam.org/articles/10.4171/rsmup/117/}
}
TY  - JOUR
AU  - Saharon Shelah
TI  - Canonical universal locally finite groups
JO  - Rendiconti del Seminario Matematico della Università di Padova
PY  - 2023
SP  - 25
EP  - 44
VL  - 149
UR  - http://archive.numdam.org/articles/10.4171/rsmup/117/
DO  - 10.4171/rsmup/117
LA  - en
ID  - RSMUP_2023__149__25_0
ER  - 
%0 Journal Article
%A Saharon Shelah
%T Canonical universal locally finite groups
%J Rendiconti del Seminario Matematico della Università di Padova
%D 2023
%P 25-44
%V 149
%U http://archive.numdam.org/articles/10.4171/rsmup/117/
%R 10.4171/rsmup/117
%G en
%F RSMUP_2023__149__25_0
Saharon Shelah. Canonical universal locally finite groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 149 (2023), pp. 25-44. doi : 10.4171/rsmup/117. http://archive.numdam.org/articles/10.4171/rsmup/117/

Cité par Sources :