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02677nam a2200469 4500 |
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978-981-13-9949-7 |
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DE-He213 |
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20191027033022.0 |
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190830s2019 si | s |||| 0|eng d |
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|a 9789811399497
|9 978-981-13-9949-7
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|a 10.1007/978-981-13-9949-7
|2 doi
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|a Cheng, Yong.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Incompleteness for Higher-Order Arithmetic
|h [electronic resource] :
|b An Example Based on Harrington's Principle /
|c by Yong Cheng.
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|a 1st ed. 2019.
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|a Singapore :
|b Springer Singapore :
|b Imprint: Springer,
|c 2019.
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|a XIV, 122 p. 1 illus.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
|2 rda
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|a SpringerBriefs in Mathematics,
|x 2191-8198
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|a 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.
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|a 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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|a Mathematical logic.
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|a Mathematical Logic and Foundations.
|0 http://scigraph.springernature.com/things/product-market-codes/M24005
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9789811399480
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|i Printed edition:
|z 9789811399503
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|i Printed edition:
|z 9789811399510
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|a SpringerBriefs in Mathematics,
|x 2191-8198
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|u https://doi.org/10.1007/978-981-13-9949-7
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a Mathematics and Statistics (Springer-11649)
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