9789811399480 - Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington?s Principle di Cheng, Yong (15 risultati)

Condizione: New. pp. 122.

Condizione: New. pp. 122.

Condizione: Brand New. New. US edition. Expediting shipping for all USA and Europe orders excluding PO Box. Excellent Customer Service.

Condizione: New. This is a Brand-new US Edition. This Item may be shipped from US or any other country as we have multiple locations worldwide.

Condizione: New. Brand New Original US Edition. Customer service! Satisfaction Guaranteed.

Condizione: New. pp. 122.

Brand new book. Fast ship. Please provide full street address as we are not able to ship to P O box address.

Condizione: New. Brand New! Fast Delivery This is an International Edition and ship within 24-48 hours. Deliver by FedEx and Dhl, & Aramex, UPS, & USPS and we do accept APO and PO BOX Addresses. Order can be delivered worldwide within 7-12 days and we do have flat rate for up to 2LB. Extra shipping charges will be requested if the Book weight is more than 5 LB. This Item May be shipped from India, United states & United Kingdom. Depending on your location and availability.

Paperback. Condizione: Brand New. 136 pages. 9.25x6.10x0.50 inches. In Stock.

Taschenbuch. Condizione: Neu. Neuware -Gödel's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A lot of research has since been done in this direction, most notably by Harvey Friedman. A lot of examples of concrete incompleteness with real mathematical content have been found to date. This brief contributes to Harvey Friedman's research program on concrete incompleteness for higher-order arithmetic and gives a specific example of concrete mathematical theorems which is expressible in second-order arithmetic but the minimal system in higher-order arithmetic to prove it is fourth-order arithmetic.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 136 pp. Englisch.

Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - Gödel's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A lot of research has since been done in this direction, most notably by Harvey Friedman. A lot of examples of concrete incompleteness with real mathematical content have been found to date. This brief contributes to Harvey Friedman's research program on concrete incompleteness for higher-order arithmetic and gives a specific example of concrete mathematical theorems which is expressible in second-order arithmetic but the minimal system in higher-order arithmetic to prove it is fourth-order arithmetic.This book first examines the following foundational question: are all theorems in classic mathematics expressible in second-order arithmetic provable in second-order arithmetic The author gives a counterexample for this question and isolates this counterexample from the Martin-Harrington Theorem in set theory. It shows that the statement 'Harrington's principle implies zero sharp' is not provable in second-order arithmetic. This book further examines what is the minimal system in higher-order arithmetic to prove the theorem 'Harrington's principle implies zero sharp' and shows that it is neither provable in second-order arithmetic or third-order arithmetic, but provable in fourth-order arithmetic. The book also examines the large cardinal strength of Harrington's principle and its strengthening over second-order arithmetic and third-order arithmetic.

Paperback. Condizione: New. NEW. SHIPS FROM MULTIPLE LOCATIONS. book.

Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Gödel's true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similarly unprovable. A lot of research has since been done in this direction, most notably by Harvey Friedman. A lot of examples of concrete incompleteness with real mathematical content have been found to date. This brief contributes to Harvey Friedman's research program on concrete incompleteness for higher-order arithmetic and gives a specific example of concrete mathematical theorems which is expressible in second-order arithmetic but the minimal system in higher-order arithmetic to prove it is fourth-order arithmetic.This book first examines the following foundational question: are all theorems in classic mathematics expressible in second-order arithmetic provable in second-order arithmetic The author gives a counterexample for this question and isolates this counterexample from the Martin-Harrington Theorem in set theory. It shows that the statement 'Harrington's principle implies zero sharp' is not provable in second-order arithmetic. This book further examines what is the minimal system in higher-order arithmetic to prove the theorem 'Harrington's principle implies zero sharp' and shows that it is neither provable in second-order arithmetic or third-order arithmetic, but provable in fourth-order arithmetic. The book also examines the large cardinal strength of Harrington's principle and its strengthening over second-order arithmetic and third-order arithmetic. 136 pp. Englisch.

Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Goedel s true-but-unprovable sentence from the first incompleteness theorem is purely logical in nature, i.e. not mathematically natural or interesting. An interesting problem is to find mathematically natural and interesting statements that are similar.

Taschenbuch. Condizione: Neu. Incompleteness for Higher-Order Arithmetic | An Example Based on Harrington's Principle | Yong Cheng | Taschenbuch | xiv | Englisch | 2019 | Springer | EAN 9789811399480 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand.