Geometric Set Theory

Cover
Title page
Copyright
Contents
Preface
Chapter 1. Introduction
	1.1. Outline of the subject
	1.2. Equivalence relation results
	1.3. Independence: by topic
	1.4. Independence: by model
	1.5. Independence: by preservation theorem
	1.6. Navigation
	1.7. Notation and terminology
Part I . Equivalence relations
	Chapter 2. The virtual realm
		2.1. Virtual equivalence classes
		2.2. Virtual structures
		2.3. Classification: general theorems
		2.4. Classification: specific examples
		2.5. Cardinal invariants
		2.6. Restrictions on partial orders
		2.7. Absoluteness
		2.8. Dichotomies
	Chapter 3. Turbulence
		3.1. Independent functions
		3.2. Examples and operations
		3.3. Placid equivalence relations
		3.4. Examples and operations
		3.5. Absoluteness
		3.6. A variation for measure
	Chapter 4. Nested sequences of models
		4.1. Prologue
		4.2. Coherent sequences of models
		4.3. Choice-coherent sequences of models
Part II . Balanced extensions of the Solovay model
	Chapter 5. Balanced Suslin forcing
		5.1. Virtual conditions
		5.2. Balanced virtual conditions
		5.3. Weakly balanced Suslin forcing
	Chapter 6. Simplicial complex forcings
		6.1. Basic concepts
		6.2. Fragmented complexes
		6.3. Matroids
		6.4. Quotient variations
	Chapter 7. Ultrafilter forcings
		7.1. A Ramsey ultrafilter
		7.2. Fubini powers of the Fréchet ideal
		7.3. Ramsey sequences of structures
		7.4. Semigroup ultrafilters
	Chapter 8. Other forcings
		8.1. Coloring graphs
		8.2. Coloring hypergraphs
		8.3. Discontinuous homomorphisms
		8.4. Automorphisms of power (gw ) modulo finite
		8.5. Kurepa families
		8.6. Set mappings
		8.7. Saturated models on quotient spaces
		8.8. Non-DC variations
		8.9. Side condition forcings
		8.10. Weakly balanced variations
	Chapter 9. Preserving cardinalities
		9.1. The well-ordered divide
		9.2. The smooth divide
		9.3. The turbulent divide
		9.4. The orbit divide
		9.5. The ????_{????_{gs }} divide
		9.6. The pinned divide
	Chapter 10. Uniformization
		10.1. Tethered Suslin forcing
		10.2. Uniformization theorems
		10.3. Examples
	Chapter 11. Locally countable structures
		11.1. Central objects and notions
		11.2. Definable control
		11.3. Centered control
		11.4. Linked control
		11.5. Measured control
		11.6. Ramsey control
		11.7. Liminf control
		11.8. Compactly balanced posets
	Chapter 12. The Silver divide
		12.1. Perfectly balanced forcing
		12.2. Bernstein balanced forcing
		12.3. ????-Bernstein balanced forcing
		12.4. Existence of generic filters
	Chapter 13. The arity divide
		13.1. ????,????-centered and balanced forcings
		13.2. Preservation theorems
		13.3. Examples
	Chapter 14. Other combinatorics
		14.1. Maximal almost disjoint families
		14.2. Unbounded linear suborders
		14.3. Measure and category
		14.4. The Ramsey ultrafilter extension
Bibliography
Index
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