9 papers · 1 filter
A proof of the Borel completeness of torsion free abelian groups
Michael C. Laskowski, Douglas S. Ulrich
A proof of the Borel completeness of torsion free abelian groups is presented. This proof differs considerably from the approach of Paolini-Shelah.
Most(?) theories have Borel complete reducts
Michael C. Laskowski, Douglas S. Ulrich
We prove that many seemingly simple theories have Borel complete reducts. Specifically, if a countable theory has uncountably many complete 1-types, then it has a Borel complete re…
Pseudosaturation and the Interpretability Orders
Douglas Ulrich
We streamline treatments of the interpretability orders of Shelah, the key new notion being that of pseudosaturation. Extending work of Malliaris and Shelah,…
Cardinal Characteristics of Models of Set Theory
Douglas Ulrich
We continue our investigation =of Shelah's interpretability orders as well as the new orders . In particular, we give streamlined pr…
A Streamlined Proof of
Douglas Ulrich
We streamline Malliaris and Shelah's proof that . In particular, we replace cofinality spectrum problems with models of , and we eliminate the u…
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 is a complete countable theory and is a complete Boolean algebra…