Classical evidence Gödel's incompleteness theorems

Filip Morić, Ilija Lalović

The classical proofs of Gödel's incompleteness theorem are presented in the paper. The incompleteness of Peano's arithmetic and Peano's arithmetic with exponentiation is proved. The relation between consistency and $\omega$-consistency is examined. The latest achievements in logic offer the possibility for proofs of Gödel's incompletenes theorem to be viewed from a new logical and mathematical viewpoint.