Shaun Allison

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math.LO2026

Classification Strength of Polish Groups: Involving $S_{\infty}$

Shaun Allison

In recent years, much work has been done to measure and compare the complexity of orbit equivalence relations, especially for certain classes of Polish groups. We start by introduc…

math.LO2026

The class and dynamics of $I^\pm$ -balanced Polish groups

Shaun Allison, Aristotelis Panagiotopoulos

For each ordinal $I^\pm < I ¨ _{1}$ , we introduce the class of $I^\pm$ -balanced Polish groups. These classes form a hierarchy that completely stratifies the space between the class of Polish g…

Classification Strength of Polish Groups: Involving S∞​

The class and dynamics of I^±-balanced Polish groups

Classification Strength of Polish Groups: Involving $S_{\infty}$

The class and dynamics of $I^\pm$ -balanced Polish groups