Extensional Gödel Functional Interpretation

Inhaltsverzeichnis

and survey.- A formal system of classical analysis.- Elimination of extensionality.- Translation of classical into intuitionistic approximated theories.- Gödel's functional interpretation in the narrower sense.- The calculus T of the primitive recursive functionals.- Functional interpretation of classical arithmetic plus (ER)-qf, (AC)-qf and functional interpretation in the narrower sense of Heyting-analysis plus (ER)-qf, (MP), in T.- The calculus T? BR of the bar recursive functionals.- Functional interpretation of classical (AC)o-, (? AC)-analysis with (ER)-qf and functional interpretation in the narrower sense of Heyting-analysis plus (ER)-qf, (MP), in T? BR.- Further consequences from the functional interpretation of classical analysis.- Consistency proof by computation. Computation of T? BRo... o??.- Generalized inductive definitions.- Generalization of bar induction BID and the inductive generation processes to trees over species.- A model for T? BR.- On the bar recursive model of classical analysis and the general bar induction over species.