Talk:Self-verifying theories
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A little more context
[edit]I posted a bit more about these theories in my Advogato diary. ---- Charles Stewart 20:29, 22 Sep 2004 (UTC)
To dos
[edit]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)