3 citations · 9 across the 12 of their papers we have counts for
16 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.
Characterizing the existence of a Borel complete expansion
Michael C. Laskowski, Douglas S. Ulrich
We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence as a class of structures in a related language. From this, we sh…
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…
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 , let be the theory o…
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…
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 of and to every cardinal , the th…
Distinct Volume Subsets via Indiscernibles
William Gasarch, Douglas Ulrich
Erdös proved that for every infinite there is with , such that all pairs of points from have distinct distances, and he gave…
Torsion-Free Abelian Groups are Consistently -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 exists, then $\mbox{TFAG}$ is -com…
Can Have Infinitely Many Classes
Saharon Shelah, Danielle Ulrich
Building off of recent results on Keisler's order, we show that consistently, has infinitely many classes. In particular, we define the property of -type amalga…
Low is a Dividing Line in Keisler's Order
Douglas Ulrich
We show in that the class of low theories forms a dividing line in Keisler's order. That is, if is low and then is low. We also show there is…
Keisler's Order is Not Linear, Assuming a Supercompact
Douglas Ulrich
We show that Keisler's order is not linear, assuming the existence of a supercompact cardinal.
The Number of Atomic Models of Uncountable Theories
Douglas Ulrich
We show there exists a complete theory in a language of size continuum possessing a unique atomic model which is not constructible. We also show it is consistent with $ZFC + \aleph…
Borel Complexity and Potential Canonical Scott Sentences
Douglas Ulrich, Richard Rast, Michael C. Laskowski
We define and investigate HC-forcing invariant formulas of set theory, whose interpretations in the hereditarily countable sets are well behaved under forcing extensions. This lead…