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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 thedoi:10.1017/bsl.2020.22 fatcat:3yjtrpretzea7ekf5h4hilnhjq