Douglas Ulrich

collaborators

7 papers

math.LO2018

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

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

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

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

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…

Pseudosaturation and the Interpretability Orders

Cardinal Characteristics of Models of Set Theory

A Streamlined Proof of p=t

Keisler's Order and Full Boolean-Valued Models

Distinct Volume Subsets via Indiscernibles

Torsion-Free Abelian Groups are Consistently aΔ21​-complete

A Streamlined Proof of $p = t$

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