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E-raamat: Constructibility

(Lancaster University)
  • Formaat: PDF+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 16-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731703
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  • Formaat: PDF+DRM
  • Sari: Perspectives in Logic
  • Ilmumisaeg: 16-Mar-2017
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781316731703
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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the L-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the J-hierarchy and the Jensen 'fine-structure theory'.

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A comprehensive account of the theory of constructible sets at an advanced level, aimed at graduate mathematicians.
Part A Elementary Theory
Chapter I Preliminaries
3(53)
1 The Language of Set Theory
3(1)
2 The Zermelo-Fraenkel Axioms
4(2)
3 Elementary Theory of ZFC
6(6)
4 Ordinal Numbers
12(1)
5 Cardinal Numbers
13(7)
6 Closed Unbounded Sets
20(2)
7 The Collapsing Lemma
22(2)
8 Metamathematics of Set Theory
24(7)
9 The Language Lv
31(13)
10 Definability
44(4)
11 Kripke-Platek Set Theory. Admissible Sets
48(8)
Chapter II The Constructible Universe
56(52)
1 Definition of the Constructible Universe
57(6)
2 The Constructible Hierarchy. The Axiom of Constructibility
63(8)
3 The Axiom of Choice in L
71(6)
4 Constructibility and Relative Consistency Results
77(1)
5 The Condensation Lemma. The GCH in L
78(7)
6 Σn Skolem Functions
85(10)
7 Admissible Ordinals
95(13)
Chapter III ω1-Trees in L
108(29)
1 The Souslin Problem. ω1-Trees. Aronszajn Trees
108(10)
2 The Kurepa Hypothesis
118(4)
3 Some Combinatorial Principles Related to the Previous Constructions
122(15)
Chapter IV κ+-Trees in L and the Fine Structure Theory
137(32)
1 κ+-Trees
137(1)
2 κ+-Souslin Trees
138(11)
3 κ+ -Kurepa Trees
149(3)
4 The Fine Structure Theory
152(6)
5 The Combinatorial Principle κ
158(11)
Chapter V The Story of 0#
169(56)
1 A Brief Review of Large Cardinals
169(7)
2 L-Indiscernibles and 0#
176(9)
3 Definability of 0#
185(3)
4 0# and Elementary Embeddings
188(8)
5 The Covering Lemma
196(29)
Part B Advanced Theory
Chapter VI The Fine Structure Theory
225(78)
1 Rudimentary Functions
225(26)
2 The Jensen Hierarchy of Constructible Sets
251(7)
3 The Σ1-Skolem Function
258(8)
4 The Σn-Projectum
266(8)
5 Standard Codes
274(10)
6 An Application: A Global-Principle
284(19)
Chapter VII Trees and Large Cardinals in L
303(29)
1 Weakly Compact Cardinals and κ-Souslin Trees
303(9)
2 Ineffable Cardinals and κ-Kurepa Trees
312(7)
3 Generalised Kurepa Families and the Priciples κ1+λ
319(13)
Chapter VIII Morasses and the Cardinal Transfer Theorem
332(51)
1 Cardinal Transfer Theorems
332(6)
2 Gap-1 Morasses
338(21)
3 The Gap-2 Cardinal Transfer Theorem
359(10)
4 Simplified Morasses
369(9)
5 Gap-n Morasses
378(5)
Chapter IX Silver Machines
383(26)
1 Silver Machines
383(8)
2 The Combinatorial Principle
391(18)
Remarks and Historical Notes 409(6)
Bibliography 415(4)
Glossary of Notation 419(3)
Index 422
Keith J. Devlin works in the Department of Mathematics at the University of Lancaster.