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A classification of incompleteness statements
Henry Towsner, James Walsh
For which choices of does no sufficiently strong -sound and -definable extension theory prove its own -soundness? We give a complete answer, ther…
Intersecting sets in probability spaces and Shelah's classification
Artem Chernikov, Henry Towsner
For and , given a sufficiently long sequence of events in a probability space all of measure at least , some of them will have…
On the equivalence of quasirandomness and exchangeable representations independent from lower-order variables
Leonardo N. Coregliano, Henry P. Towsner
It is often convenient to represent a process for randomly generating a graph as a graphon. (More precisely, these give \emph{vertex exchangeable} processes -- those processes in w…
Perfect stable regularity lemma and slice-wise stable hypergraphs
Artem Chernikov, Henry Towsner
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of…