Proof Theory: An Introduction (Lecture Notes in Mathematics, 1407)

Pohlers, Wolfram; Pohlers

ISBN 10: 3540518428 / ISBN 13: 9783540518426

Editore: Springer (edition ), 1989

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Codice articolo 3540518428-7-1

Dati bibliografici

• Titolo: Proof Theory: An Introduction (Lecture Notes in Mathematics, 1407)
• Editore: Springer (edition )
• Data di pubblicazione: 1989
• Lingua: Inglese
• ISBN 10: 3540518428
• ISBN 13: 9783540518426
• Rilegatura: Paperback
• Condizione: Fair

Descrizione articolo

Riassunto

Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

Contenuti

Ordinal Analysis of Pure Number Theory.- The autonomous ordinal of the infinitary system Z? and the limits of predicativity.- Ordinal analysis of the formal theory for noniterated inductive definitions.