Douglas Ulrich

activity

20142022

most citedKeisler's Order and Full Boolean-Valued Models

3 citations · 9 across the 12 of their papers we have counts for

collaborators

Showing 2018Show all

9 papers · 1 filter

math.LO2018★ 2 cited

Pseudosaturation and the Interpretability Orders

Douglas Ulrich

We streamline treatments of the interpretability orders $⊴_{κ}^{*}$ of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah,…

math.LO2018★ 2 cited

Cardinal Characteristics of Models of Set Theory

Douglas Ulrich

We continue our investigation =of Shelah's interpretability orders $⊴_{κ}^{*}$ as well as the new orders $⊴_{κ}^{\times}$ . In particular, we give streamlined pr…

math.LO2018★ 1 cited

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 $2 \leq k < n < ω$ , let $T_{n, k}$ be the theory o…

math.LO2018

A Streamlined Proof of $p = t$

Douglas Ulrich

We streamline Malliaris and Shelah's proof that $p = t$ . In particular, we replace cofinality spectrum problems with models of $Z F C^{-}$ , and we eliminate the u…

math.LO2018★ 3 cited

Keisler's Order and Full Boolean-Valued Models

Douglas Ulrich

We prove a compactness theorem for full Boolean-valued models. As an application, we show that if $T$ is a complete countable theory and $B$ is a complete Boolean algebra…

math.LO2018

Borel Complexity and the Schröder-Bernstein Property

Danielle Ulrich

We introduce a new invariant of Borel reducibility, namely the notion of thickness; this associates to every sentence $Φ$ of $L_{ω_{1} ω}$ and to every cardinal $λ$ , the th…

math.LO2018

Distinct Volume Subsets via Indiscernibles

William Gasarch, Douglas Ulrich

Erdös proved that for every infinite $X \subseteq R^{d}$ there is $Y \subseteq X$ with $∣ Y ∣ = ∣ X ∣$ , such that all pairs of points from $Y$ have distinct distances, and he gave…

math.LO2018

Torsion-Free Abelian Groups are Consistently $a Δ_{2}^{1}$ -complete

Saharon Shelah, Douglas Ulrich

Let $\mbox{TFAG}$ be the theory of torsion-free abelian groups. We show that if there is no countable transitive model of $Z F C^{-} + κ (ω)$ exists, then $\mbox{TFAG}$ is $a Δ_{2}^{1}$ -com…

math.LO2018

$\leq_{S P}$ 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…

Pseudosaturation and the Interpretability Orders

Cardinal Characteristics of Models of Set Theory

Amalgamation and Keisler's Order

A Streamlined Proof of p=t

Keisler's Order and Full Boolean-Valued Models

Borel Complexity and the Schröder-Bernstein Property

Distinct Volume Subsets via Indiscernibles

Torsion-Free Abelian Groups are Consistently aΔ21​-complete

≤SP​ Can Have Infinitely Many Classes

A Streamlined Proof of $p = t$

Torsion-Free Abelian Groups are Consistently $a Δ_{2}^{1}$ -complete

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