Scott Mutchnik

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5 papers · 1 filter

math.LO2026

A counterexample to the stable forking conjecture

James Freitag, Scott Mutchnik

Using ChatGPT 5.6, we find a counterexample to the stable forking conjecture. This answers a long-standing open question of Hart, Kim and Pillay (1996).

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.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…

math.LO2024

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…