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Re: Size of ordinal for ordinal definable real
Posted:
Dec 29, 2013 4:09 AM


dullrich@sprynet.com writes:
> Exactly what is an "ordinal definable real"? What does this have to > do with phi. In what sense does phi(x, alpha) "hold"?
In settheorist speak, a set A is said to be ordinal definable if there is a formula P(y, x1, ..., xn), in the firstorder language of settheory, so that for some ordinals alpha(1), ..., alpha(n), A = {y  P(y, alpha(1), ..., alpha(n)}. And obvs here a real is, naturally enough, a set of naturals, as per the usual custom of settheory land.
 Aatu Koskensilta (aatu.koskensilta@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"  Ludwig Wittgenstein, Tractatus LogicoPhilosophicus



