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math.LO2026
Some model-theoretic consequences of high-arity uniform convergence, part I
Leonardo N. Coregliano, Maryanthe Malliaris
We show that certain families of sets in (or ) which are neither definable nor have bounded VC-dimension are nonetheless uniformly approximately defina…
math.LO2025
Remarks on a recent preprint of Chernikov and Towsner
Maryanthe Malliaris
In this brief note, we first give a counterexample to a theorem in Chernikov and Towsner, arXiv:2510.02420(1). In arXiv:2510.02420(2), the theorem has changed but as we explain the…
math.LO2025
On ultrafilter construction
Maryanthe Malliaris
We give a model-theoretic perspective on regular ultrafilter construction in the twentieth and twenty-first century (so far), and explain the "canonical Boolean algebra" recently d…
math.LO2018
Model theory and ultraproducts
M. Malliaris
The article motivates recent work on saturation of ultrapowers from a general mathematical point of view.