Invariant measures in simple and in small theories
A Chernikov, E Hrushovski, A Kruckman… - … of Mathematical Logic, 2023 - World Scientific
Journal of Mathematical Logic, 2023•World Scientific
We give examples of (i) a simple theory with a formula (with parameters) which does not fork
over∅ but has μ-measure 0 for every automorphism invariant Keisler measure μ and (ii) a
definable group G in a simple theory such that G is not definably amenable, ie 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.
over∅ but has μ-measure 0 for every automorphism invariant Keisler measure μ and (ii) a
definable group G in a simple theory such that G is not definably amenable, ie 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.
We give examples of (i) a simple theory with a formula (with parameters) which does not fork over but has -measure 0 for every automorphism invariant Keisler measure and (ii) a definable group in a simple theory such that is not definably amenable, i.e. there is no translation invariant Keisler measure on . 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.
World Scientific以上显示的是最相近的搜索结果。 查看全部搜索结果