# Sh:1029

- Shelah, S. (2016).
*No universal group in a cardinal*. Forum Math.,**28**(3), 573–585. arXiv: 1311.4997 DOI: 10.1515/forum-2014-0040 MR: 3510831 -
Abstract:

For many classes of models, there are universal members in any cardinal \lambda which “essentially satisfies GCH, i.e. \lambda = 2^{< \lambda}", in particular for the class of a complete first order T (well, if at least if \lambda > |T|). But if the class is “complicated enough", e.g. the class of linear orders, we know that if \lambda is “regular and not so close to satisfying GCH" then there is no universal member. Here we find new sufficient conditions (which we call the olive property), not covered by earlier cases (i.e. fail the so-called \rm SOP_4). The advantage of those conditions is witnessed by proving that the class of groups satisfies one of those conditions.This version has minor changes , compared to the earlier one.

- Version 2024-01-24_2 (20p) published version (13p)

Bib entry

@article{Sh:1029, author = {Shelah, Saharon}, title = {{No universal group in a cardinal}}, journal = {Forum Math.}, fjournal = {Forum Mathematicum}, volume = {28}, number = {3}, year = {2016}, pages = {573--585}, issn = {0933-7741}, mrnumber = {3510831}, mrclass = {03C45 (03C50 03C55 03C65 03E04 03E75 20A15)}, doi = {10.1515/forum-2014-0040}, note = {\href{https://arxiv.org/abs/1311.4997}{arXiv: 1311.4997}}, arxiv_number = {1311.4997} }