| Autor: |
Conley, Clinton, Jahel, Colin, Panagiotopoulos, Aristotelis |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
Countable $\mathcal{L}$-structures $\mathcal{N}$ whose isomorphism class supports a permutation invariant probability measure in the logic action have been characterized by Ackerman-Freer-Patel to be precisely those $\mathcal{N}$ which have no algebraicity. Here we characterize those countable $\mathcal{L}$-structure $\mathcal{N}$ whose isomorphism class supports a quasi-invariant probability measure. These turn out to be precisely those $\mathcal{N}$ which are not "highly algebraic" -- we say that $\mathcal{N}$ is highly algebraic if outside of every finite $F$ there is some $b$ and a tuple $\bar{a}$ disjoint from $b$ so that $b$ has a finite orbit under the pointwise stabilizer of $\bar{a}$ in $\mathrm{Aut}(\mathcal{N})$. As a bi-product of our proof we show that whenever the isomorphism class of $\mathcal{N}$ admits a quasi-invariant measure, then it admits one with continuous Radon--Nikodym cocycles. |
| Databáze: |
arXiv |
| Externí odkaz: |
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