ИСТИНА

In the talk we will present a new generalisation of G¨odel second incompleteness theorem. We introduce a theory Syn(Ω) that talks about first-order formulas of a given signature Ω. We prove the Diagonal Lemma and G¨odel second incompleteness theorem for all theories T that interpret theory Syn(Ω), where Ω is the signature of T. We note that unlike more standard approaches that are applicable only to some arithmetical theories (or theories that interpret certain arithmetical theory), our approach is applicable to a wider class of theories – all theories that interpret the theory of pairing function on an infinite domain.