Defines α-balanced Polish groups stratifying TSI and CLI, establishes closure properties and coanalytic rank, and constructs actions with strong generic ergodicity against lower levels via generic α-unbalancedness.
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2 Pith papers cite this work. Polarity classification is still indexing.
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Non-Archimedean Polish groups involve S_∞ exactly when they satisfy a weakened disjoint amalgamation property, a weakened absolute generating indiscernibles property, or lack ordinal rank in a coanalytic rank function, and only such groups classify the benchmark equivalence relation =+.
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The class and dynamics of $\alpha$-balanced Polish groups
Defines α-balanced Polish groups stratifying TSI and CLI, establishes closure properties and coanalytic rank, and constructs actions with strong generic ergodicity against lower levels via generic α-unbalancedness.
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Classification Strength of Polish Groups: Involving $S_\infty$
Non-Archimedean Polish groups involve S_∞ exactly when they satisfy a weakened disjoint amalgamation property, a weakened absolute generating indiscernibles property, or lack ordinal rank in a coanalytic rank function, and only such groups classify the benchmark equivalence relation =+.