LIBERO WebOPAC Catalogue Display (W561)

Catalogue Information
Field name	Details
Dewey Class	511.3
Title	Incompleteness for Higher-Order Arithmetic ([EBook]) : An Example Based on Harrington’s Principle / by Yong Cheng.
Author	Cheng, Yong
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2019.
Publication	Singapore : Springer Singapore , 2019.
Physical Details	XIV, 122 pages: 1 illus. : online resource.
Series	SpringerBriefs in Mathematics
ISBN	9789811399497
Summary Note	The book examines the following foundation question: are all theorems in classic mathematics which are expressible in second order arithmetic provable in second order arithmetic? In this book, the author gives a counterexample for this question and isolates this counterexample from Martin-Harrington theorem in set theory. It shows that the statement “Harrington’s principle implies zero sharp” is not provable in second order arithmetic. The book also examines what is the minimal system in higher order arithmetic to show that Harrington’s principle implies zero sharp and the large cardinal strength of Harrington’s principle and its strengthening over second and third order arithmetic. .:
Contents note	Introduction and Preliminary -- A minimal system -- The Boldface Martin-Harrington Theorem in Z2 -- Strengthenings of Harrington’s Principle -- Forcing a model of Harrington’s Principle without reshaping -- The strong reflecting property for L-cardinals.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	https://doi.org/10.1007/978-981-13-9949-7
Links to Related Works	Subject References: Mathematical logic . Mathematical Logic and Foundations . Authors: author . Cheng, Yong . Corporate Authors: SpringerLink (Online service) . Series: SpringerBriefs in Mathematics . Classification: 511.3 . 511.3 (DDC 23) .

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Incompleteness for Higher-Order Arithmetic: An Example Based on Harrington’s Principle

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