Sh:1186

• Džamonja, M., & Shelah, S. (2021). On wide Aronszajn trees in the presence of MA. J. Symb. Log., 86(1), 210–223. arXiv: 2002.02396 DOI: 10.1017/jsl.2020.42 MR: 4282706
• Abstract:
  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 the same assumption there is no universal Aronszajn tree, improving a result of Todorčević from 2007 who proved the same under the assumption of BPFA for posets of size \aleph_1. Finally, we prove that under MA(\omega_1), every wide Aronszajn tree weakly embeds in an Aronszajn tree.
• Version 2020-06-03_3 (16p) published version (14p)

@article{Sh:1186,
 author = {D{\v{z}}amonja, Mirna and Shelah, Saharon},
 title = {{On wide Aronszajn trees in the presence of MA}},
 journal = {J. Symb. Log.},
 fjournal = {The Journal of Symbolic Logic},
 volume = {86},
 number = {1},
 year = {2021},
 pages = {210--223},
 issn = {0022-4812},
 mrnumber = {4282706},
 mrclass = {03E05 (03E35 03E50)},
 doi = {10.1017/jsl.2020.42},
 note = {\href{https://arxiv.org/abs/2002.02396}{arXiv: 2002.02396}},
 arxiv_number = {2002.02396}
}