Yong Cheng

Incompleteness for Higher-Order Arithmetic (eBook, PDF)

An Example Based on Harrington's Principle

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Springer Nature Singapore
• Seitenzahl: 122
• Erscheinungstermin: 30. August 2019
• Englisch
• ISBN-13: 9789811399497
• Artikelnr.: 57608224

Inhaltsangabe

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.