2 citations · 2 across the 8 of their papers we have counts for
8 papers
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).
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…
Some applications of the real strict order property hierarchy
Scott Mutchnik
We give applications of the properties for non-integer values of to problems on the original hierarchy for integer values of . We fir…
Approximations of the strict order property
Scott Mutchnik
We observe that the definition of Shelah's classical hierarchy for first-order theories, for integers , can be restated so that it extends to the case…
Simple Homogeneous Structures and Indiscernible Sequence Invariants
John Baldwin, James Freitag, Scott Mutchnik
We introduce some properties describing dependence in indiscernible sequences: and its dual , the definable Morley property, and -resolvability. Applying these…
Properties of independence in theories
Scott Mutchnik
We prove some results about the theory of independence in theories that do not hold in theories. We generalize Chernikov's work on simple an…
Conant-independence and generalized free amalgamation
Scott Mutchnik
We initiate the study of a generalization of Kim-independence, Conant-independence, based on the "strong Kim-dividing" of Kaplan, Ramsey and Shelah. We introduce an axiom on statio…
Generic expansions and the group configuration theorem
Scott Mutchnik
We exhibit a connection between geometric stability theory and the classification of unstable structures at the level of simplicity and the - g…