Re: Lowenheim-Skolem-Ockham Theorem

Torkel Franzen wrote: 
Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx> writes:

No. But omega^CK_1 is still inherently impredicative and the upper bound of where you can get autonomously (in the sense outlined in the above quote).

What makes Gamma_0 impredicative, if we can get to it autonomously?

"We" can get to it autonomously only in the above mentioned sense. Not in any epistemologically interesting sense. My guess was that that was why Bill considered L_omega^CK_1 a natural "stopping point".

Of course, one could consider Gamma_0 predicative, since there is a recursive ordering of that type. But it isn't predicatively recognizable as a well-ordering (or schematic transfinite induction for it isn't predicatively acceptable or however you express it).

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

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