当前位置: X-MOL 学术J. Symb. Log. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
ON WIDE ARONSZAJN TREES IN THE PRESENCE OF MA
The Journal of Symbolic Logic ( IF 0.6 ) Pub Date : 2020-09-07 , DOI: 10.1017/jsl.2020.42
MIRNA DŽAMONJA , SAHARON SHELAH

A wide Aronszajn tree is a tree of size and height $\omega _{1}$ with no uncountable branches. We prove that under $MA(\omega _{1}\!)$ there is no wide Aronszajn tree which is universal under weak embeddings. This solves an open question of Mekler and Väänänen from 1994.We also prove that under $MA(\omega _{1}\!)$ , every wide Aronszajn tree weakly embeds in an Aronszajn tree, which combined with a result of Todorčević from 2007, gives that under $MA(\omega _{1}\!)$ every wide Aronszajn tree embeds into a Lipschitz tree or a coherent tree. We also prove that under $MA(\omega _{1}\!)$ there is no wide Aronszajn tree which weakly embeds all Aronszajn trees, improving the result in the first paragraph as well as a result of Todorčević from 2007 who proved that under $MA(\omega _{1}\!)$ there are no universal Aronszajn trees.

中文翻译:

MA 在场的 ARONSZAJN 大树上

宽大的 Aronszajn 树是大小和高度的树$\欧米茄_{1}$没有不可数的分支。我们证明在$MA(\omega _{1}\!)$没有在弱嵌入下通用的宽 Aronszajn 树。这解决了 Mekler 和 Väänänen 从 1994 年开始提出的一个悬而未决的问题。我们还证明了$MA(\omega _{1}\!)$,每棵宽的 Aronszajn 树都弱嵌入到 Aronszajn 树中,结合 2007 年的 Todorčević 的结果,得出以下结论$MA(\omega _{1}\!)$每棵宽大的 Aronszajn 树都嵌入到 Lipschitz 树或连贯树中。我们还证明了在$MA(\omega _{1}\!)$不存在弱嵌入所有 Aronszajn 树的宽 Aronszajn 树,改进了第一段中的结果以及 Todorčević 从 2007 年开始证明的结果$MA(\omega _{1}\!)$没有通用的 Aronszajn 树。
更新日期:2020-09-07
down
wechat
bug