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An ordinal is the order type of a well-ordered set. The first few ordinals are $0, 1, 2, \dots, \omega, \omega+1, \dots$ where $\omega$ is the order type of $\mathbb{N}$, and $\omega+1$ is the order type of $\mathbb{N}$ together with a maximum element.

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An ordinal not $\Sigma_1$ stable in alpha must be in the hull of smaller parameters in $L_\a...

This concerns an assertion of Sy Friedman in [1], Lemma 2, which claims that, under certain conditions, if $\beta$ is not 0 and not $\Sigma_1$-stable in $\alpha$, i.e. $L_\beta\prec_1 L_\alpha$, then …
Chris Le Sueur's user avatar