Scott Mutchnik

collaborators

5 papers

math.LO2026

Reducing stable forking dependence to finitely many pregeometries

Scott Mutchnik

We show that one of the main cases of the stable forking conjecture, stability of the forking relation over a base in a finite-rank supersimple theory, is determined by finitely ma…

math.LO2026

Some applications of the real strict order property hierarchy

Scott Mutchnik

We give applications of the properties $NSOP_{r}$ for non-integer values of $r$ to problems on the original hierarchy $NSOP_{n}$ for integer values of $n$ . We fir…

math.LO2026

Properties of independence in $NSOP_{3}$ theories

Scott Mutchnik

We prove some results about the theory of independence in $NSOP_{3}$ theories that do not hold in $NSOP_{4}$ theories. We generalize Chernikov's work on simple an…

math.LO2026

Simple Homogeneous Structures and Indiscernible Sequence Invariants

John Baldwin, James Freitag, Scott Mutchnik

We introduce some properties describing dependence in indiscernible sequences: $F_{in d}$ and its dual $F_{M b}$ , the definable Morley property, and $n$ -resolvability. Applying these…

math.LO2025

Approximations of the strict order property

Scott Mutchnik

We observe that the definition of Shelah's classical $NSOP_{n}$ hierarchy for first-order theories, for integers $n \geq 3$ , can be restated so that it extends to the case…

Reducing stable forking dependence to finitely many pregeometries

Some applications of the real strict order property hierarchy

Properties of independence in NSOP3​ theories

Simple Homogeneous Structures and Indiscernible Sequence Invariants

Approximations of the strict order property

Properties of independence in $NSOP_{3}$ theories