Gap ordinal: Difference between revisions
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A gap ordinal is an ordinal \(\alpha\) such that \((L_{\alpha+1}\setminus L_\alpha)\cap\mathcal P(\omega)=\varnothing\).<ref name="MarekSrebrny73">W. Marek, M. Srebrny, "[https://www.sciencedirect.com/science/article/pii/0003484374900059 Gaps in the Constructible Universe]" (1973). Annals of Mathematical Logic vol. 6, pp.359--394.</ref><sup>p.364</sup> An ordinal \(\alpha\) is said to start a gap if \(\alpha\) is a gap ordinal but for all \(\beta<\alpha\), \((L_\alpha\setminus L_\beta)\cap\mathcal P(\omega)\neq\varnothing\).<ref name="MarekSrebrny73" /><sup>p.368</sup>
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