2021/05/15 by Artem Chernikov, Chernikov, Artem, Ehud Hrushovski +11
Mathematics · #03C45 #43A07 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2105.07281
openalex publication_date 2021/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over the empty set but has mu measure 0 for every automorphism invariant Keisler measure mu, and (ii) a definable group G in a simple theory such that G is not definably amenable, i.e. there is no translation invariant Keisler measure on G We also discuss paradoxical decompositions both in the setting of discrete groups and of definable groups, and prove some positive results about small theories, including the definable amenability of definable groups, and nontriviality of the graded Grothendieck ring.