[FOM] constructible sets
Aatu Koskensilta
Aatu.Koskensilta at uta.fi
Thu Feb 25 15:32:18 EST 2010
Quoting jbell at uwo.ca:
> Can someone answer the following question: does V = L follow from the
> assertion that every subset of every constructible set is constructible?
Yes.
> Maybe I'm missing something obvious!
Prove it by induction. Suppose that V_alpha is constructible for all
alpha < beta. By your assertion, every element of V_beta is
constructible, since it is a subset of V_alpha for some alpha < beta.
Take now the supremum of the constructible ranks of elements of V_beta
to obtain a suitable level of L, and conclude that V_beta is
constructible.
--
Aatu Koskensilta (aatu.koskensilta at uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
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