Incompleteness for higher order arithmetic : An Example Based on Harrington’s Principle
2019 ed.
by
Yong Cheng
Book Details
Format
Paperback / Softback
Book Series
SpringerBriefs in Mathematics
ISBN-10
9811399484
ISBN-13
9789811399480
Edition
2019 ed.
Publisher
Springer Verlag, Singapore
Imprint
Springer Verlag, Singapore
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Sep 11th, 2019
Print length
122 Pages
Product Classification:
Mathematical foundationsMathematical logic
Ksh 9,900.00
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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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