2018 seminar talk: New aspects of ladder system uniformization

Talk held by Daniel Soukup (KGRC) at the KGRC seminar on 2018-11-29.


After a brief overview of some classical results, we will survey new applications of ladder system uniformization. In particular, we constrast uniformizations defined on $\omega_1$ and uniformizations on trees of height $\omega_1$. The latter, introduced by J. Moore, played a critical role in understanding minimal uncountable linear orders under CH. One of our rather surprising new results is that whenever $\diamondsuit^+$ holds, for any ladder system $\mathbf C$ there is an Aronszajn tree $T$ so that any monochromatic colouring of $\mathbf C$ has a $T$-uniformization (cf. https://arxiv.org/abs/1806.03867).

A video recording of this talk is available on YouTube.

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