Absoluteness.

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Article #496

#496

From: Bill Taylor
Date: Fri, 18 Dec 1992 03:44

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Several times I thought I have understood the technical logical term "absolute".
But each time I leave the book thinking I know what it is, then the next day
find I can't remember it any more.   Perhaps the net folk will have more
success than the text books, driving it into my thick skull.  

So...

1) What does it mean for a set theoretic concept to be "absolute".

2) Could you briefly outline why, in particular, "being an ordinal" is
   absolute, but "being a cardinal" is not (or at least "having the same
   cardinality" is not.

3) Does (2) have anything at all to do with the recently-noted-here fact that
   in ZF- it is not possible to define a cardinal, though it is to define an
   ordinal. 

Thanks.     Bill Taylor.         wft@math.canterbury.ac.nz

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Path: arc1-ca.pugleaf.net!sparky!uunet!wupost!waikato.ac.nz!canterbury.ac.nz!math!wft
Newsgroups: sci.logic
Subject: Absoluteness.
Message-ID: <BzFrpK.DBC@cantua.canterbury.ac.nz>
From: wft@math.canterbury.ac.nz (Bill Taylor)
Date: Fri, 18 Dec 1992 03:44:07 GMT
Organization: Department of Mathematics, University of Canterbury
Nntp-Posting-Host: sss330.canterbury.ac.nz
Lines: 18