Re: question

From: Rupert <rupertmccallum@xxxxxxxxx>
Date: 27 May 2007 03:42:41 -0700

On May 27, 5:12 pm, Rupert <rupertmccal...@xxxxxxxxx> wrote:

Can it be proved in ZF that every Tarski infinite set admits a partial
ordering without a maximal element?

Based on the Wikipedia article, it would seem not.

http://en.wikipedia.org/wiki/Finite_set

I am trying to do the following problem. Given a first-order language
L with equality whose only extralogical symbol is a binary predicate
symbol, find a sentence S in L such that S has no finite models, and
if U is an infinite set, then there exists a binary relation P on U
such that the structure <U,P> is a model of S. Is there a solution to
this problem in ZF?

.

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