Abstract:We introduce the notions of $rgs$ and $irgs$ for Keisler measures, motivated by the study of generically stable random types and their associated Morley sequences. We obtain characterizations of these notions in terms of averages of classical first-order formulas over suitable probabilistic partitions (Theorems 3.2 and 3.3). We compare these notions with $fim$, $fam$, and self-averaging, and show that for types the notions $fim$, $irgs$, and $rgs$ coincide. We prove that every $irgs$ measure is dependent (Theorem 4.5); consequently, such measures are symmetric (Corollary 4.8). Furthermore, we show that for $irgs$ measures the model-theoretic instability events $\mathbf{O}^\varphi$, $\mathbf{I}^\varphi$, and $\mathbf{L}^\varphi$ have $\mathbb{P}_\mu$-measure zero (Theorem~5.4), extending results from [8] beyond the $fim$ case.
From: Karim Khanaki [view email]
[v1]
Fri, 15 May 2026 11:39:23 UTC (19 KB)
[v2]
Fri, 29 May 2026 10:39:47 UTC (23 KB)
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