2 papers
math.LO2026
On the notion of a patterning property in model theory
Gabriel Day, Scott Mutchnik
Different kinds of definable patterns in the models of a first-order theory, such as the order property, the tree property, or the (-)strict order property, allow us to distingu…
math.LO2024
An theory without the existence axiom
Scott Mutchnik
Answering a question of Dobrowolski, Kim and Ramsey, we find an theory that does not satisfy the existence axiom.