Assertion: set's subset | /r/PartOf | l ω
Facets:
Source sentences:
text: All arithmetical subsets of ω and relations on ω belong to L ω +1 (because the arithmetic definition gives one in L ω +1 ).
text: Conversely, any subset of ω belonging to L ω +1 is arithmetical (because elements of L ω can be coded by natural numbers in such a way that ∈ is definable, i.e., arithmetic).
text: _{1}^{\mathrm {CK} }} stands for the Church–Kleene ordinal), and conversely any subset of ω that belongs to L ω 1