Courier 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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abstract antecedent applied arbitrary arity assigned assume auxiliary formulas axiom of choice bound variables called comprehension axioms consistency proof constructive contains countable cut formula cut-elimination theorem cut-free deﬁned deﬁned as follows DEFINITION denoted determinate logic eigenvariable conditions end-piece end-sequent exists ﬁgure ﬁnite ﬁrst order ﬁxed free variables Friedman Gentzen’s Godel number hence heterogeneous quantiﬁers homogeneous impredicative induction hypothesis inﬁnitary inﬁnite initial sequents intuitionistic j-section j-subsection Kreisel language Lemma limit ordinal lower sequent Math mathematical mathematical induction method natural numbers notation obtained occurs order free variable ordinal analysis ordinal diagram outermost logical symbol Peano arithmetic predicate constant primitive recursive function principal formula proof theory proof-theoretic Proposition proved RCAO reduction replacing respectively Reverse Mathematics satisﬁes second order arithmetic second order variable semi-formula set theory structure subformulas subset substitution subsystems succedent Suppose Takeuti transﬁnite induction upper sequent Vx A(x well-ordering