Announcement of a paper by R.M. Causey
1 Jan
2020
1 Jan
'20
3:06 p.m.
This is an announcement for the paper “$Sz(\cdot)\leqslant ω^ξ$ is rarely a three space property” by R.M. Causey<https://arxiv.org/search/math?searchtype=author&query=Causey%2C+R+M>. Abstract: We prove that for any non-zero, countable ordinal $\xi$ which is not additively indecomposable, the property of having Szlenk index not exceeding $\omega^\xi$ is not a three space property. This complements a result of Brooker and Lancien, which states that if $\xi$ is additively indecomposable, then having Szlenk index not exceeding $\omega^\xi$ is a three space property. https://arxiv.org/abs/1912.13429
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Bentuo Zheng (bzheng)