[FOM] Explicit constructions

[John T. Baldwin]

JoeShipman at aol.com wrote:

>In a message dated 7/3/2003 3:01:09 PM Eastern Standard Time, jbaldwin at uic.edu writes:
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>>One of the important discoveries of the middle 20th century is the
>>futility of a trying to find a general foundations of 
>>mathematics.
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Shipman asks:

>>In what sense is the usual foundations via ZFC "futile"?  Is there a part of mathematics it cannot provide a foundation for?  Or does it have some other irreparable inadequacy?
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Baldwin replies:

ZFC is quite successful has providing a groundwork for mathematics.  But 
rather than providing a context for investigating `foundational questions'
in mathematics as practiced it has become another branch of mathematics 
(replace `model theory' by `set theory' in Friedman's characterization of
Baldwin's view of model theory.)

The general explanation by model theorists of the Borel Tits Theorem is 
a more
direct contribution to the foundations of algebraic geometry and group 
representations than results about measurable cardinals.
(See Poizat: Stable groups  Chapter 4.)


 (Incidentially, some one more knowkedgeable could easily come up with 
example from recent work in descriptive set theory which  is just as 
good an example of a contribution to the foundations of analysis or 
group representations.)

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