Proof TheoryCourier Corporation, 2013/01/01 - 490 ページ This comprehensive monographis a cornerstone in the area ofmathematical logic and relatedfields. Focusing on Gentzen-typeproof theory, the book presents adetailed overview of creative works by the author and other20th-century logicians that includes applications of prooftheory to logic as well as other areas of mathematics.Reprint of the North Holland, Amsterdam, 1987 edition. |
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a₁ an+1 analysis antecedent applied arbitrary arity assume auxiliary formulas axiom of choice b₁ bound variables C₁ called comprehension axiom consistency proof constructive contains countable cut formula cut-elimination theorem cut-free cut-free proof defined denoted end-piece end-sequent exists F₁ finite formal free variables Gentzen's Gödel Gödel number hence impredicative in+1 induction hypothesis inductive definitions inference infinitary infinitary logic initial sequents iterated j-section Kreisel language Lemma limit ordinal lower sequent mathematical mathematical induction natural numbers notation obtained occurs ordinal analysis ordinal diagram outermost logical symbol predicate calculus predicate constant primitive recursive function principal formula proof theory proof-theoretic PROPOSITION provable proved reduction respectively S₁ satisfies second order variable set theory subformulas subset subsystems succedent Suppose t₁ transfinite induction upper sequent well-ordering Γ₁ ΓΔ