Re: Godel misuses ZF

you say

Gosh! Really? I wonder if the obviously erudite and technically competent
Dean would like to explain to us exactly what the so-called
Skolem Paradox is, and exactly why it shows ZF to be inconsistent. I
wait with bated breath for more words of wisdom ..

i say
http://en.wikipedia.org/wiki/Skolem's_paradox

In mathematical logic, specifically set theory, Skolem's paradox is a
direct result of the (downward) Löwenheim-Skolem theorem, which states
that every model of a sentence of a first-order language has an
elementarily equivalent countable submodel.

Using the Löwenheim-Skolem Theorem, we can get a model of set theory
which only contains a countable number of objects. However, it must
contain the aforementioned uncountable sets, which appears to be a
contradiction--[note the word contradiction which makes ZF inconsistent]

The paradox is seen in Zermelo-Fraenkel (ZF) set theory.


even Abraham Fraenkel
says its a contradiction

"Neither have the books yet been closed on the antinomy, nor has agreement
on its significance and possible solution yet been reached." â?? (Abraham
Fraenkel)


Skolem's result applies only to the first-order interpretation of
Zermelo-Fraenkel set theory, but Zermelo considered this first-order
interpretation to be flawed and fraught with "finitary prejudice".

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