Incompleteness for Higher-Order Arithmetic An Example Based on Harrington’s Principle
Başlık:
Incompleteness for Higher-Order Arithmetic An Example Based on Harrington’s Principle
Yazar:
Cheng, Yong. author.
ISBN:
9789811399497
Yazar:
Edisyon:
1st ed. 2019.
Fiziksel Niteleme:
XIV, 122 p. 1 illus. online resource.
Seri:
SpringerBriefs in Mathematics,
İçindekiler:
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.
Özet:
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. .
Ek Kurum Yazar:
Elektronik Erişim:
https://doi.org/10.1007/978-981-13-9949-7