This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G�del's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, in particular the Dialectica interpretation and its generalization to finite types, the Diller-Nahm interpretation, are studied on Heyting as well as Peano arithmetic in finite types and extended to functional interpretations of constructive as well as classical systems of analysis and set theory. Kreisel's modified realization and Troelstra's hybrids of it are presented as interpretations of Heyting arithmetic and extended to constructive set theory, both in finite types. They serve as background for the construction of hybrids of the Diller-Nahm interpretation of Heyting arithmetic and constructive set theory, again in finite types. All these functional interpretations yield relative consistency results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.

From the Back Cover

This book gives a detailed treatment of functional interpretations of arithmetic, analysis, and set theory. The subject goes back to G del's Dialectica interpretation of Heyting arithmetic which replaces nested quantification by higher type operations and thus reduces the consistency problem for arithmetic to the problem of computability of primitive recursive functionals of finite types. Regular functional interpretations, i.e. Dialectica and Diller Nahm interpretation as well as Kreisel's modified realization, together with their Troelstra-style hybrids, are applied to constructive as well as classical systems of arithmetic, analysis, and set theory. They yield relative consistency and conservativity results and closure under relevant rules of the theories in question as well as axiomatic characterizations of the functional translations.

Prerequisites are: familiarity with classical and intuitionistic predicate logic, basics of computability theory, G del's incompleteness theorems.

"About this title" may belong to another edition of this title.

Store Description

GreatBookPrices.com is your top source for finding new books at the absolute lowest prices, guaranteed ! We offer big discounts - everyday - on millions of titles in virtually any category, from Architecture to Zoology -- and everything in between. Discover great deals and super-savings, on professional books, text book titles, the newest computer guides, or your favorite fiction authors. You'll find it all - at HUGE SAVINGS - at GreatBookPrices. Browse through our complete online product catalog today. Serving customers around the world for years, we help thousands find just the books they're looking for -- at incredibly low, bargain prices.

Visit Seller's Storefront

Seller's business information

Far Corner Europe Limited
19-20 Bourne Court, 19-20 Bourne Court, Woodford Green, IG8 8HD, United Kingdom

Sale & Shipping Terms

Terms of Sale

Company Name: GreatBookPricesUK
Legal Entity: Far Corner Europe Limited
Address: 19-20 Bourne Court, Southend Road, Woodford Green Essex, UK IG8 8HD
Registration #: 10691061
Authorized representative: Danielle Hainsey

Shipping Terms

Our warehouses across the globe are fully operational without substantial delays. We are working hard and continue to overcome the daily challenges presented by COVID-19. There have been reports that delivery carriers are experiencing large delays resulting in longer than normal deliveries to customers. See USPS's website for further detail. We would like to apologize in advance if your item arrives later than the expected delivery due date.

Internal processing of your order will take about 1-2 business days. Please allow an additional 4-14 business days for Media Mail delivery. We have multiple ship-from locations - MD,IL,NJ,UK,IN,NV,TN & GA

Shipping rates from United Kingdom to U.S.A.

Shipping rates from United Kingdom to U.S.A.
Order quantity	10 to 30 business days	10 to 27 business days
First item	US$ 19.97	US$ 19.97

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.