[FOM] constructible sets

[Aatu Koskensilta]

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