关于自由代数与模理论的评注
逻辑
2020-04-28 v2 环与代数
摘要
我们提出一些问题并对（完备）理论T(infinity, V)做一些观察，该理论为V中无限生成元上的自由代数，其中V是泛代数意义下的簇。我们聚焦于T(infinity, R)的情形，其中V是R-模的簇（R为环）。基于Kucera-Pillay的工作，我们刻画了何时T(infinity, R)的所有模型都是自由的、投射的、平坦的，以及T(infinity,R)何时在更高基数上范畴化。
引用
@article{arxiv.2004.10351,
title = {Remarks on theories of free algebras and modules},
author = {Anand Pillay and Philipp Rothmaler},
journal= {arXiv preprint arXiv:2004.10351},
year = {2020}
}
备注
10 pages. In this new version we clarify the status of the conjecture of Tarski that we heard about from Baldwin. Actually the paper of Baldwin and Lachlan referred to in the paper already gives a counterexample to the conjecture, although we give another one which is possibly more natural: a variety of R-modules