On the definability of mad families of vector spaces

Haim Horowitz; Saharon Shelah

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arXiv · 1811.03753

On the definability of mad families of vector spaces

Haim Horowitz·Saharon Shelah

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Abstract

We consider the definability of mad families in vector spaces of the form $\underset{n<\omega}{\bigoplus} F$ where $F$ is a field of cardinality $\leq \aleph_0$. We show that there is no analytic mad family of subspaces when $F=\mathbb{F}_2$, partially answering a question of Smythe. Our proof relies on a variant of Mathias forcing restricted to a certain idempotent ultrafilter whose existence follows from Glazer's proof of Hindman's theorem.

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Haim Horowitz, Saharon Shelah. 2018-11-09. On the definability of mad families of vector spaces. https://arxiv.org/abs/1811.03753

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