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express similar sentiments. Hamkins writes that the book is "full of historical insight, clear writing, interesting theorems, and elegant proofs". Because this topic uses many of the important tools of set theory more generally, Lévy recommends the book "to anybody who wants to start doing research
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in their series
Perspectives in Mathematical Logic, with a second edition in 2003 in their Springer Monographs in Mathematics series, and a paperback reprint of the second edition in 2009 (
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Although quotations expressing the philosophical positions of researchers in this area appear throughout the book, more detailed coverage of issues in the
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Reviewer Pierre Matet writes that this book "will no doubt serve for many years to come as the main reference for large cardinals", and reviewers
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Next are two chapters on "Forcing and sets of reals" and "Aspects of measurability". The main topic of the first of these chapters is
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to prove the consistency of measurable cardinals, and related results using stronger notions of forcing.
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and the theory of infinite games. Reviewer Frank R. Drake views this chapter, and the proof in it by
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The Higher
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in set theory", and Welch recommends it to all university libraries.
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Chapter five is "Strong hypotheses". It includes material on
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In the first chapter, "Beginnings", the material includes
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The second chapter, "Partition properties", includes the
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study of large cardinals, and the existence of the set
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90:constructible universe
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187:reflection properties
98:elementary embeddings
378:Mathematical Reviews
211:axiom of determinacy
199:extendible cardinals
78:measurable cardinals
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280:Hamkins, Joel David
195:Vopěnka's principle
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151:. It also includes
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242:Joel David Hamkins
121:partition calculus
104:, and a result of
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176:Robert M. Solovay
153:Jónsson cardinals
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185:and their
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