Re: Axiom of infinity and the set of all hereditary finite sets.
- From: Aatu Koskensilta <aatu.koskensilta@xxxxxxxxx>
- Date: 29 Sep 2007 20:57:27 +0300
Zaljohar@xxxxxxxxx writes:
Can you give me an example of a set x such that the set
{x,Ux,UUx,UUUx,.....} is infinite.
Yes: the set of finite von Neumann ordinals, omega. Incidentally,
{x,Ux,UUx,UUUx,.....} is not the transitive closure of x -- its union
is.
Why do you think the existence of sets with infinite transitive
closure, or, equivalently, the existence of infinite transitive sets,
contradicts regularity?
--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)
"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.
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