Incompleteness for Higher-Order Arithmetic / SpringerBriefs in Mathematics (PDF)

Name: Incompleteness for Higher-Order Arithmetic / SpringerBriefs in Mathematics
Brand: Springer-Verlag GmbH
SKU: 127996762
Price: 21.99 EUR
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An Example Based on Harrington's Principle (Sprache: Englisch)

Autor: Yong Cheng

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Incompleteness for Higher-Order Arithmetic / SpringerBriefs in Mathematics, Yong Cheng

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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.