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Topic: Size of ordinal for ordinal definable real
Replies: 9   Last Post: Jan 2, 2014 10:50 AM

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Aatu Koskensilta

Posts: 2,631
Registered: 6/28/08
Re: Size of ordinal for ordinal definable real
Posted: Dec 29, 2013 5:01 AM
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Peter Percival <peterxpercival@hotmail.com> writes:

> Suppose phi(x,alpha) is a formula of ZFC (or your favourite set
> theory) such that for all real x there is an ordinal alpha such that
> phi(x,alpha) holds. (I.e. x is an ordinal definable real.) How big
> does alpha need to be?


In the constructible universe, a new real (set of naturals) appears at
each countable level.

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

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



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