Talk:Self-verifying theories

A little more context
I posted a bit more about these theories in my Advogato diary. Charles Stewart 20:29, 22 Sep 2004 (UTC)

To dos
There were a few minor problems with added text (notably these theories are not in the same language as PA, since they cannot have multiplication as a function symbol).

I've also polished the article a bit more, and while it is clearly incomplete, I think it isn't a "cleanup" article any more, so I changed its status to "stub", and I think it doesn't need much work to leave this status.

What needs doing:
 * The language of Willard's systems needs to be given formally;
 * Solovay's arguments showing totality of varying classes of function leads to the diagonalisation argument needs to be outlined, together with a reconiliation with the pparent contradiction of some of these;
 * The construction of the tableau sentence;
 * The change in arithmetic complexity between PA and this system should be described (ie. many Pi-0-1 sentences of PA are Pi-0-2 sentences of Willard's system);
 * References: JSL paper, FOL75 paper, Solovay's negative results.

Hope to get around to it soon ... Charles Stewart 12:31, 29 Sep 2004 (UTC)