[FOM] Model theory and foundations IV

John T. Baldwin jbaldwin at uic.edu
Wed Jul 9 22:08:35 EDT 2003

Friedman writes:

However, consider real closed fields. There is intricate set theoretic 
information at every uncountable cardinal, because of the order. Would 
you consider a necessarily set theoretic study of the structure of 
uncountable real closed fields part of model theory?

Baldwin replies.  This seems to be a misconception, real closed fields 
are essentially ordered. The study of their orderings is model theory by 
any standard.   I.e. I see no justification for `necessarily set 
theoretic study' in the previous comment.

 (I have some recollection that this was largely settled by Abraham 
Robinson 40 years ago.  Maybe someone has
more precise information).

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