FOM: Completion of previous posting

[JoeShipman@aol.com]

This is a repost because my comments on the first paper, below, were cut
 off.  WARNING: When you send a post to FOM, do not repeat DO NOT include
 any text lines which consist of a single period.  They are interpreted
 by Steve Simpson's web server's stupid e-mail software as denoting "end
 of message" and all further content is truncated. -- JS
 
 
 
Thanks to Adrian Mathias for another excellent posting.  The Casacuberta, 
Scevenfels and Smith paper "Implications of large-cardinal principles in 
homotopical localization" can be downloaded at
 
 http://manwe.mat.uab.es/casac/vopenka.ps
 
 , and the Contents and first chapter of Woodin's new book "The Axiom of
 Determinacy, Forcing Axioms and the Nonstationary Ideal" is at
 
 http://www.degruyter.de/pdf/woodin.pdf
 
 
 I am especially interested in the first paper because
 
 1) Vopenka's Principle is one of my favorite large cardinal axioms, since it 
is better motivated and easier to state than almost all of them 
(inaccessibles and measurables are easier still, but I can't think of any 
others that are easier).
 
 2) This is a use of large cardinals to settle an open problem in "ordinary 
mathematics" (excluding logic, foundations, set theory).  Have there been any 
other good examples of this since Solovay's work on real-valued measurables?  
(I don't count Friedman's work because although its latest incarnation 
certainly looks like "ordinary mathematics" it does not touch on any 
questions that had previously been 
 investigated and regarded as unsolved.)
 
 - Joe Shipman