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).
New aspects of ladder system uniformizationI
29.11.2018 15:00 - 16:30
Organiser:
KGRC
Location:
SR 101, 2. St., Währinger Str. 25