An introduction to proof theory normalization, cut-elimination, and consistency proofs / Paolo Mancosu, Sergio Galvan, Richard Zach.
| Author/creator | Mancosu, Paolo |
| Other author | Galvan, Sergio, 1946- |
| Other author | Zach, Richard. |
| Other author | Oxford University Press. |
| Format | Electronic |
| Edition | First edition. |
| Publication Info | New York, NY : Oxford University Press, 2021. |
| Description | xii, 418 pages : illustrations ; 25 cm |
| Supplemental Content | Full text available from Oxford Scholarship Online |
| Subjects |
| Abstract | "Proof theory is a central area of mathematical logic of special interest to philosophy . It has its roots in the foundational debate of the 1920s, in particular, in Hilbert's program in the philosophy of mathematics, which called for a formalization of mathematics, as well as for a proof, using philosophically unproblematic, "finitary" means, that these systems are free from contradiction. Structural proof theory investigates the structure and properties of proofs in different formal deductive systems, including axiomatic derivations, natural deduction, and the sequent calculus. Central results in structural proof theory are the normalization theorem for natural deduction, proved here for both intuitionistic and classical logic, and the cut-elimination theorem for the sequent calculus. In formal systems of number theory formulated in the sequent calculus, the induction rule plays a central role. It can be eliminated from proofs of sequents of a certain elementary form: every proof of an atomic sequent can be transformed into a "simple" proof. This is Hilbert's central idea for giving finitary consistency proofs. The proof requires a measure of proof complexity called an ordinal notation. The branch of proof theory dealing with mathematical systems such as arithmetic thus has come to be called ordinal proof theory. The theory of ordinal notations is developed here in purely combinatorial terms, and the consistency proof for arithmetic presented in detail"-- Provided by publisher. |
| Bibliography note | Includes bibliographical references (pages 405-411) and index. |
| Access restriction | Available only to authorized users. |
| Technical details | Mode of access: World Wide Web |
| Genre/form | Electronic books. |
| LCCN | 2021910782 |
| ISBN | 9780192895936 (hardback) |
| ISBN | 9780192895943 (paperback) |
| ISBN | (ebook) |
Availability
| Library | Location | Call Number | Status | Item Actions |
|---|---|---|---|---|
| Electronic Resources | Access Content Online | ✔ Available |