Talk:Rowbottom cardinal

Equivalent property
On p. 5 of Mitchell's "Inner Models for Large Cardinals" I found that there is a model-theoretic characterization of Rowbottomness of $$\kappa$$, however I cannot find Mitchell's characterization in either The Higher Infinite or Rowbottom's paper. Theorem 2.1 in Rowbottom's paper does almost give a model-theoretic characterization of $$\lambda$$-Rowbottom cardinals (written as $$\mathcal C_\omega(\kappa,\lambda,\kappa,\lambda)$$ in the terminology of the paper), but not quite, as for the theorem to apply to $$\lambda$$-Rowbottomness, the quintuple $$\omega,\kappa,\lambda,\kappa,\lambda$$ would have to be relevant, but $$\kappa>\lambda>\lambda\geq\omega$$ fails. Is anyone aware of a source for either of these or any similar characterizations in order to add them? C7XWiki (talk) 07:32, 12 May 2024 (UTC)