Extensional Gödel Functional Interpretation
A Consistensy Proof of Classical Analysis
Published on 9. January 1973
Book
Paperback/Softback
VI, 166 pages
978-3-540-06119-9 (ISBN)
Description
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.
More details
Series
Edition
1973 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
VI, 166 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 10 mm
Weight
271 gr
ISBN-13
978-3-540-06119-9 (9783540061199)
DOI
10.1007/BFb0060871
Schweitzer Classification
Content
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.