GÖDEL'S SECOND INCOMPLETENESS THEOREM: HOW IT IS DERIVED AND WHAT IT DELIVERS

SAEED SALEHI
2020 Bulletin of Symbolic Logic  
The proofs of Gödel (1931) , Rosser (1936) , Kleene (first 1936 and second 1950 ), Chaitin (1970 for the first incompleteness theorem are compared with each other, especially from the viewpoint of the second incompleteness theorem. It is shown that Gödel's (first incompleteness theorem) and Kleene's first theorems are equivalent with the second incompleteness theorem, Rosser's and Kleene's second theorems do deliver the second incompleteness theorem, and Boolos' theorem is derived from the
more » ... rived from the second incompleteness theorem in the standard way. It is also shown that none of Rosser's, Kleene's second or Boolos' theorems is equivalent with the second incompleteness theorem, and Chaitin's incompleteness theorem neither delivers nor is derived from the second incompleteness theorem. We compare (the strength of) these six proofs with one another.
doi:10.1017/bsl.2020.22 fatcat:3yjtrpretzea7ekf5h4hilnhjq