The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some...(展开全部)

The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive account of the theory of large cardinals from its beginnings and some...(展开全部)

This is the softcover reprint of the very popular hardcover edition. The theory of large cardinals is currently a broad mainstream of modern set theory, the main area of investigation for the analysis of the relative consistency of mathematical propositions and possible new axioms for mathematics. The first of a projected multi-volume series, this book provides a comprehensive ...(展开全部)

After describing the beginnings of the subject - the theory of large cardinals - a comprehensive account is given of the work in the 1960s on partition properties, forcing and sets of reals, and aspects of measurability (including saturated ideals and inner models of measurability). Then discussed are the strong hypotheses like supercompactness up to Kunen's inconsistency. The ...(展开全部)

This book is designed for readers who know elementary mathematical logic and axiomatic set theory, and who want to learn more about set theory. The primary focus of the book is on the independence proofs. Most famous among these is the independence of the Continuum Hypothesis (CH); that is, there are models of the axioms of set theory (ZFC) in which CH is true, and other models...(展开全部)

This introduction to modern set theory covers all aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, desriptive set theory, and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater influence on mathematics. The author'...(展开全部)

This introduction to modern set theory covers all aspects of its two main general areas: classical set theory including large cardinals, infinitary combinatorics, desriptive set theory, and independence proofs starting with Goedel's proof around 1938 followed by Cohen's proof in 1963, whereby Cohen's method of forcing probably had a greater influence on mathematics. The author'...(展开全部)

A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book...(展开全部)

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In "Higher Topos Theory", Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and...(展开全部)

Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In "Higher Topos Theory", Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and...(展开全部)