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Topic: Size of ordinal for ordinal definable real
Replies: 1   Last Post: Dec 29, 2013 4:09 AM

 Aatu Koskensilta Posts: 2,631 Registered: 6/28/08
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 set-theorist speak, a set A is said to be ordinal definable if
there is a formula P(y, x1, ..., xn), in the first-order language of
set-theory, 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 set-theory land.

--
Aatu Koskensilta (aatu.koskensilta@uta.fi)

"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus