I see now that my sketch proof of "completeness" for Rob Arthan's proposed new "new_specification" cannot be turned into a rigorous proof.
When withness are obtained using the choice function, they may fail the fourth of his specified constraints on the witnesses. They will do so in just the kinds of case which Rob was particularly interested in, viz. those in which the constants are characterised through some universal property. If the extension is conservative then there must be values for all the constants in every model of the theory being extended, but possibly there might not be terms which denote those values. Whether the new "new_specification" is or is not "complete" (in the sense which I identified) is now (once again) unclear to me. My purported "obvious proof" of completeness is fallacious, but its failure does not yield a proof of incompleteness. Roger Jones ------------------------------------------------------------------------------ Live Security Virtual Conference Exclusive live event will cover all the ways today's security and threat landscape has changed and how IT managers can respond. Discussions will include endpoint security, mobile security and the latest in malware threats. http://www.accelacomm.com/jaw/sfrnl04242012/114/50122263/ _______________________________________________ hol-info mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/hol-info
