國立虎尾科技大學 |

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

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Incompleteness for Higher-Order Arithmetic/ by Yong Cheng.
其他題名:	An Example Based on Harrington’s Principle /
作者:	Cheng, Yong.
面頁冊數:	XIV, 122 p. 1 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Mathematical logic. -
電子資源:	https://doi.org/10.1007/978-981-13-9949-7
ISBN:	9789811399497

Incompleteness for Higher-Order Arithmetic = An Example Based on Harrington’s Principle /
Cheng, Yong.

Incompleteness for Higher-Order ArithmeticAn Example Based on Harrington’s Principle /[electronic resource] :by Yong Cheng. - 1st ed. 2019. - XIV, 122 p. 1 illus.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

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.

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. .

ISBN: 9789811399497

Standard No.: 10.1007/978-981-13-9949-7doiSubjects--Topical Terms:

810627
Mathematical logic.

LC Class. No.: QA8.9-10.3

Dewey Class. No.: 511.3

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