Model-Theoretic Logics

Contents
List of Contributors
Part A. Introduction, Basic Theory and Examples
	Chapter I. Model-Theoretic Logics: Background and Aims
		1. Logics Embodying Mathematical Concepts
		2. Abstract Model Theory
		3. Conclusion
	Chapter II. Extended Logics: The General Framework
		1. General Logics
		2. Examples of Principal Logics
		3. Comparing Logics
		4. Lindstrom Quantifiers
		5. Compactness and Its Neighbourhood
		6. Lowenheim-Skolem Properties
		7. Interpolation and Definability
	Chapter III. Characterizing Logics
		1. Lindstrom's Characterizations of First-Order Logic
		2. Further Characterizations of ℒωω
		3. Characterizing ℒ∞ω
		4. Characterizing Cardinality Quantifiers
		5. A Lindstrom-Type Theorem for Invariant Sentences
Part B. Finitary Languages with Additional Quantifiers
	Chapter IV. The Quantifier "There Exist Uncountably Many" and Some of Its Relatives
		1. Introduction to ℒ(Qα)
		2. A Framework for Reducing to First-Order Logic
		3. ℒ(Q1) and ℒω1ω(Q1): Completeness and Omitting Types Theorems
		4. Filter Quantifiers Stronger Than Q1: Completeness, Compactness, and Omitting Types
		5. Extensions of if  ℒ(Q1) by Quantifiers Asserting the Existence of Certain Uncountable Sets
		6. Interpolation and Preservation Questions
		7. Appendix (An Elaboration of Section 2)
	Chapter V. Transfer Theorems and Their Applications to Logics
		1. The Notions of Transfer and Reduction
		2. The Classical Transfer Theorems
		3. Two-Cardinal Theorems and the Method of Identities
		4. Singular Cardinal-like Structures
		5. Regular Cardinal-like Structures
		6. Self-extending Models
		7. Final Remarks
	Chapter VI. Other Quantifiers: An Overview
		1. Quantifiers from Partially Ordered Prefixes
		2. Quantifiers for Comparing Structures
		3. Cardinality, Equivalence, Order Quantifiers and All That
		4. Quantifiers from Robinson Equivalence Relations
	Chapter VII. Decidability and Quantifier-Elimination
		1. Quantifier-Elimination
		2. Interpretations
		3. Dense Systems
Part C. Infinitary Languages
	Chapter VIII. ℒω1ω and Admissible Fragments
		PART I. COMPACTNESS LOST
		1. Introduction to Infinitary Logics
		2. Elementary Equivalence
		3. General Model-Theoretic Properties
		4. "Harder" Model Theory
		PART II. COMPACTNESS REGAINED
		5. Admissibility
		6. General Model-Theoretic Properties with Admissibility
		7. "Harder" Model Theory with Admissibility
		8. Extensions of ifWlC0 by Propositional Connectives
		Appendix
	Chapter IX. Larger Infinitary Languages
		1. The Infinitary Languages ℒkλ and ℒ∞λ
		2. Basic Model Theory: Counterexamples
		3. Basic Model Theory: The Lowenheim-Skolem Theorems
		4. The Back-and-Forth Method
	Chapter X. Game Quantification
		1. Infinite Strings of Quantifiers
		2. Projective Classes and the Approximations of the Game Formulas
		3. Model Theory for Game Logics
		4. Game Quantification and Local Definability Theory
	Chapter XI Applications to Algebra
		1. Universal Locally Finite Groups
		2. Subdirectly Irreducible Algebras
		3. Lefschetz's Principle
		4. Abelian Groups
		5. Almost-Free Algebras
		6. Concrete Algebraic Constructions
		7. Miscellany
PartD. Second-Order Logic
	Chapter XII. Definable Second-Order Quantifiers
		1. Definable Second-Order Quantifiers
		2. Only Four Second-Order Quantifiers
		3. Infinitary Monadic Logic and Generalized Products
		4. The Comparison of Theories
		5. The Classification of Theories by Interpretation of Second-Order Quantifiers
		6. Generalizations
	Chapter XIII. Monadic Second-Order Theories
		1. Monadic Quantification
		2. The Automata and Games Decidability Technique
		3. The Model-Theoretic Decidability Technique
		4. The Undecidability Technique
		5. Historical Remarks and Further Results
Part E. Logics of Topology and Analysis
	Chapter XIV. Probability Quantifiers
		1. Logic with Probability Quantifiers
		2. Completeness Theorems
		3. Model Theory
		4. Logic with Conditional Expectation Operators
		5. Open Questions and Research Problems
	Chapter XV. Topological Model Theory
		1. Topological Structures
		2. The Interpolation Theorem
		3. Preservation and Definability
		4. The Logic ℒtω1ω
		5. Some Applications
		6. Other Structures
	Chapter XVI. Borel Structures and Measure and Category Logics
		1. Borel Model Theory
		2. Axiomatizability and Consequences for Category and Measure Logics
		3. Completeness Theorems
Part F. Advanced Topics in Abstract Model Theory
	Chapter XVII. Set-Theoretic Definability of Logics
		1. Model-Theoretic Definability Criteria
		2. Set-Theoretic Definability Criteria
		3. Characterizations of Abstract Logics
		4. Other Topics
	Chapter XVIII. Compactness, Embeddings and Definability
		1. Compact Logics
		2. The Dependence Number
		3. ℒ-Extensions and Amalgamation
		4. Definability
	Chapter XIX. Abstract Equivalence Relations
		1. Logics with the Robinson Property
		2. Abstract Model Theory for Enriched Structures
		3. Duality Between Logics and Equivalence Relations
		4. Duality Between Embedding and Equivalence Relations
		5. Sequences of Finite Partitions, Global and Local Back-and-Forth Games
	Chapter XX. Abstract Embedding Relations
		1. The Axiomatic Framework
		2. Amalgamation
		3. ω-Presentable Classes
Bibliography