home *** CD-ROM | disk | FTP | other *** search
/ NetNews Usenet Archive 1992 #23 / NN_1992_23.iso / spool / sci / math / 12905 < prev    next >
Encoding:
Internet Message Format  |  1992-10-09  |  1.3 KB
  1. Path: sparky!uunet!europa.asd.contel.com!darwin.sura.net!jvnc.net!netnews.upenn.edu!sagi.wistar.upenn.edu
  2. From: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
  3. Newsgroups: sci.math
  4. Subject: Re: consequences of the Axiom of Choice
  5. Message-ID: <92147@netnews.upenn.edu>
  6. Date: 8 Oct 92 14:58:07 GMT
  7. References: <1akbpqINN8hk@usenet.INS.CWRU.Edu> <1992Oct5.192243.17318@guinness.idbsu.edu> <91826@netnews.upenn.edu> <1992Oct6.214824.4955@guinness.idbsu.edu>
  8. Sender: news@netnews.upenn.edu
  9. Reply-To: weemba@sagi.wistar.upenn.edu (Matthew P Wiener)
  10. Organization: The Wistar Institute of Anatomy and Biology
  11. Lines: 11
  12. Nntp-Posting-Host: sagi.wistar.upenn.edu
  13. In-reply-to: holmes@opal.idbsu.edu (Randall Holmes)
  14.  
  15. In article <1992Oct6.214824.4955@guinness.idbsu.edu>, holmes@opal (Randall Holmes) writes:
  16. >And, alas, the prime ideal theorem is false in Solovay's model (it
  17. >implies the existence of non-measurable sets).
  18.  
  19. I've never quite understood the philosophy behind this "alas".  People
  20. who don't like AC usually do so because they like constructive proofs.
  21. Most constructive work keeps one within the realm of the measurable.
  22. The only exception that I know of, where knowledge and sometimes even
  23. use of PCA say exists, is probability.
  24. -- 
  25. -Matthew P Wiener (weemba@sagi.wistar.upenn.edu)
  26.