Douglas Ulrich

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math.LO2024

Amalgamation and Keisler's Order

Danielle Ulrich

Malliaris and Shelah famously proved that Keisler's order $⊴$ has infinitely many classes. In more detail, for each $2 \leq k < n < I ¨ $ , let $T_{n, k}$ be the theory…

math.LO2024

$\leq_{S P}$ Can Have Infinitely Many Classes

Saharon Shelah, Danielle Ulrich

Building off of recent results on Keisler's order, we show that consistently, $\leq_{S P}$ has infinitely many classes. In particular, we define the property of $\leq k$ -type amalga…

math.LO2024

Borel Complexity and the SchrÃ¶der-Bernstein Property

Danielle Ulrich

We introduce a new invariant of Borel reducibility, namely the notion of thickness; this associates to every sentence $I^¦$ of $L_{I ¨ _{1} I ¨ }$ and to every cardinal $I^»$ , th…

Amalgamation and Keisler's Order

≤SP​ Can Have Infinitely Many Classes

Borel Complexity and the SchrÃ¶der-Bernstein Property

$\leq_{S P}$ Can Have Infinitely Many Classes