# On first order amenability

@article{Hrushovski2020OnFO, title={On first order amenability}, author={Ehud Hrushovski and Krzysztof Krupinski and Anand Pillay}, journal={arXiv: Logic}, year={2020} }

We introduce the notion of first order [extreme] amenability, as a property of a first order theory $T$: every complete type over $\emptyset$, in possibly infinitely many variables, extends to an automorphism-invariant global Keisler measure [type] in the same variables. [Extreme] amenability of $T$ will follow from [extreme] amenability of the (topological) group $Aut(M)$ for all sufficiently large $\aleph_{0}$-homogeneous countable models $M$ of $T$ (assuming $T$ to be countable), but is…

## 6 Citations

### Ramsey theory and topological dynamics for first order theories

- MathematicsTransactions of the American Mathematical Society
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We investigate interactions between Ramsey theory, topological dynamics, and model theory. We introduce various Ramsey-like properties for first order theories and characterize them in terms of the…

### Automorphism invariant measures and weakly generic automorphisms

- MathematicsMathematical Logic Quarterly
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Let A$\mathcal {A}$ be a countable ℵ0‐homogeneous structure. The primary motivation of this work is to study different amenability properties of (subgroups of) the automorphism group…

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. 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…

### Amenability, connected components, and definable actions

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We study amenability of definable groups and topological groups, and prove various results, briefly described below. Among our main technical tools, of interest in its own right, is an elaboration on…

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- MathematicsArch. Math. Log.
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It is shown that if $G$ is definable over $A$ in a hereditarily G-compact theory, then $G^{00}_A=G^{000} _A$.

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