Muutke küpsiste eelistusi

E-raamat: Geometric Set Theory

,
Teised raamatud teemal:
  • Formaat - PDF+DRM
  • Hind: 185,64 €*
  • * hind on lõplik, st. muud allahindlused enam ei rakendu
  • Lisa ostukorvi
  • Lisa soovinimekirja
  • See e-raamat on mõeldud ainult isiklikuks kasutamiseks. E-raamatuid ei saa tagastada.
Geometric Set TheorySuurem pilt
Teised raamatud teemal:

DRM piirangud

  • Kopeerimine (copy/paste):

    ei ole lubatud

  • Printimine:

    ei ole lubatud

  • Kasutamine:

    Digitaalõiguste kaitse (DRM)
    Kirjastus on väljastanud selle e-raamatu krüpteeritud kujul, mis tähendab, et selle lugemiseks peate installeerima spetsiaalse tarkvara. Samuti peate looma endale  Adobe ID Rohkem infot siin. E-raamatut saab lugeda 1 kasutaja ning alla laadida kuni 6'de seadmesse (kõik autoriseeritud sama Adobe ID-ga).

    Vajalik tarkvara
    Mobiilsetes seadmetes (telefon või tahvelarvuti) lugemiseks peate installeerima selle tasuta rakenduse: PocketBook Reader (iOS / Android)

    PC või Mac seadmes lugemiseks peate installima Adobe Digital Editionsi (Seeon tasuta rakendus spetsiaalselt e-raamatute lugemiseks. Seda ei tohi segamini ajada Adober Reader'iga, mis tõenäoliselt on juba teie arvutisse installeeritud )

    Seda e-raamatut ei saa lugeda Amazon Kindle's. 

This book introduces a new research direction in set theory: the study of models of set theory with respect to their extensional overlap or disagreement. In Part I, the method is applied to isolate new distinctions between Borel equivalence relations. Part II contains applications to independence results in Zermelo-Fraenkel set theory without Axiom of Choice. The method makes it possible to classify in great detail various paradoxical objects obtained using the Axiom of Choice; the classifying criterion is a ZF-provable implication between the existence of such objects. The book considers a broad spectrum of objects from analysis, algebra, and combinatorics: ultrafilters, Hamel bases, transcendence bases, colorings of Borel graphs, discontinuous homomorphisms between Polish groups, and many more. The topic is nearly inexhaustible in its variety, and many directions invite further investigation.
Preface ix
Chapter 1 Introduction
1(32)
1.1 Outline of the subject
1(1)
1.2 Equivalence relation results
2(3)
1.3 Independence: by topic
5(5)
1.4 Independence: by model
10(2)
1.5 Independence: by preservation theorem
12(3)
1.6 Navigation
15(10)
1.7 Notation and terminology
25(8)
Part I Equivalence relations
33(70)
Chapter 2 The virtual realm
35(38)
2.1 Virtual equivalence classes
35(2)
2.2 Virtual structures
37(2)
2.3 Classification: general theorems
39(2)
2.4 Classification: specific examples
41(4)
2.5 Cardinal invariants
45(13)
2.6 Restrictions on partial orders
58(3)
2.7 Absoluteness
61(3)
2.8 Dichotomies
64(9)
Chapter 3 Turbulence
73(20)
3.1 Independent functions
73(2)
3.2 Examples and operations
75(3)
3.3 Placid equivalence relations
78(1)
3.4 Examples and operations
79(4)
3.5 Absoluteness
83(3)
3.6 A variation for measure
86(7)
Chapter 4 Nested sequences of models
93(10)
4.1 Prologue
93(1)
4.2 Coherent sequences of models
93(3)
4.3 Choice-coherent sequences of models
96(7)
Part II Balanced extensions of the Solovay model
103(220)
Chapter 5 Balanced Suslin forcing
105(12)
5.1 Virtual conditions
105(3)
5.2 Balanced virtual conditions
108(6)
5.3 Weakly balanced Suslin forcing
114(3)
Chapter 6 Simplicial complex forcings
117(18)
6.1 Basic concepts
117(1)
6.2 Fragmented complexes
117(7)
6.3 Matroids
124(4)
6.4 Quotient variations
128(7)
Chapter 7 Ultrafilter forcings
135(10)
7.1 A Ramsey ultrafilter
135(1)
7.2 Fubini powers of the Frechet ideal
136(2)
7.3 Ramsey sequences of structures
138(3)
7.4 Semigroup ultrafilters
141(4)
Chapter 8 Other forcings
145(34)
8.1 Coloring graphs
145(3)
8.2 Coloring hypergraphs
148(9)
8.3 Discontinuous homomorphisms
157(2)
8.4 Automorphisms of (ω) modulo finite
159(1)
8.5 Kurepa families
160(2)
8.6 Set mappings
162(3)
8.7 Saturated models on quotient spaces
165(4)
8.8 Non-DC variations
169(1)
8.9 Side condition forcings
170(3)
8.10 Weakly balanced variations
173(6)
Chapter 9 Preserving cardinalities
179(34)
9.1 The well-ordered divide
179(3)
9.2 The smooth divide
182(6)
9.3 The turbulent divide
188(5)
9.4 The orbit divide
193(12)
9.5 The EKσ divide
205(6)
9.6 The pinned divide
211(2)
Chapter 10 Uniformization
213(14)
10.1 Tethered Suslin forcing
213(1)
10.2 Uniformization theorems
214(7)
10.3 Examples
221(6)
Chapter 11 Locally countable structures
227(42)
11.1 Central objects and notions
227(6)
11.2 Definable control
233(4)
11.3 Centered control
237(7)
11.4 Linked control
244(6)
11.5 Measured control
250(4)
11.6 Ramsey control
254(4)
11.7 Liminf control
258(4)
11.8 Compactly balanced posets
262(7)
Chapter 12 The Silver divide
269(30)
12.1 Perfectly balanced forcing
269(5)
12.2 Bernstein balanced forcing
274(11)
12.3 n-Bernstein balanced forcing
285(7)
12.4 Existence of generic filters
292(7)
Chapter 13 The arity divide
299(14)
13.1 m, n-centered and balanced forcings
299(1)
13.2 Preservation theorems
300(7)
13.3 Examples
307(6)
Chapter 14 Other combinatorics
313(10)
14.1 Maximal almost disjoint families
313(1)
14.2 Unbounded linear suborders
314(1)
14.3 Measure and category
315(3)
14.4 The Ramsey ultrafilter extension
318(5)
Bibliography 323(6)
Index 329
Paul B. Larson, Miami University, Oxford, OH

Jindrich Zapletal, University of Florida, Gainesville, FL, and Czech Academy of Sciences, Prague, Czech Republic
Lisainfo e-raamatute kohta Lisainfo e-raamatute kohta
Püsilink: https://www.kriso.ee/db/97814704601812e.html
Märksõnad: