Almost disjoint families and some automorphic and injective properties of $\ell_\infty/c_0$

Speaker(s)

Małgorzata Rojek

Affiliation

Doctoral School of Exact and Natural Sciences UW

Language of the talk

English

Date

Oct. 15, 2025, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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The question whether any isomorphism between two isomorphic copies of $c_0(\omega_1)$ in $\ell_\infty/c_0$ can be extended to an automorphism of the whole space was posed by A. Aviles, F. Cabello Sanchez, J. Castillo, M. Gonzalez and Y. Moreno. During the talk, I will show that the answer to this problem is independent of ZFC.
If there is a maximal almost disjoint family of cardinality $\omega_1$, we use almost disjoint families to construct two copies of $c_0(\omega_1)$ which contradict the hypothesis. On the other hand, under a version of Martin’s axiom, for any isomorphism between two copies of $c_0(\kappa)$ in $\ell_\infty/c_0$, for any $\kappa < 2^\omega$, we build its automorphic extension.
This is a joint work with Piotr Koszmider, preprint available at https://arxiv.org/abs/2509.22376

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