most recent 30 from http://mathoverflow.net 2013-06-18T20:57:41Z http://mathoverflow.net/feeds/user/7142 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/29774/derivation-rules-and-godel-theorem/29802#29802 Pierre Simon 2010-06-28T15:16:57Z 2010-06-28T15:16:57Z

<p>Here is another way to answer your question: by Cons(T), you mean the consistency of the first order theory generated by the set T of axioms. But the theory ZFC+ is not first order any more, since you have added a new inference rule. So it is not true that ZFC+ proves its consistency.</p>

http://mathoverflow.net/questions/29774/derivation-rules-and-godel-theorem/29802#29802 Pierre Simon 2010-06-28T16:58:25Z 2010-06-28T16:58:25Z

So you seem to define D by : from T, conclude Cons(A,T,Der). Where Der is defined by the logic obtained from first order by adding rule D. But then nothing is well defined.