Extensional Gödel functional interpretation : a consistency proof of classical analysis

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Extensional Gödel functional interpretation : a consistency proof of classical analysis

Horst Luckhardt

(Lecture notes in mathematics, 306)

Springer-Verlag, 1973

  • : u.s.
  • : gw

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Note

Bibliography: p. 157-161

Description and Table of Contents

Table of Contents

and survey.- A formal system of classical analysis.- Elimination of extensionality.- Translation of classical into intuitionistic approximated theories.- Goedel'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.

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