This is a question from Stephan Belniuk's very good free online book "A Problem Course in Mathematical Logic":


Problem 18.6. Suppose *Sigma*  is a recursive set of sentences of LN.
Find a sentence of LN, which we'll denote by Con(*Sigma*), such that *Sigma*  is
consistent if and only if A |- Con(*Sigma*).

By Godel's second incompleteness theorem isn't this impossible?