Author | Fraรฏssรฉ, Roland. author |
---|---|
Title | Course of Mathematical Logic [electronic resource] : Volume 2 Model Theory / by Roland Fraรฏssรฉ |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 1974 |
Connect to | http://dx.doi.org/10.1007/978-94-010-2097-8 |
Descript | XX, 198 p. online resource |
1/Local Isomorphism and Logical Formula; Logical Restriction Theorem -- 1.1. (k,p)-Isomorphism -- 1.2. (k,p)-Equivalence -- 1.3. Characteristic of a Logical Formula. Relations Between (k,p) -Isomorphism and Logical Formula -- 1.4. Logical Extension and Logical Restriction; Logical Restriction Theorem -- 1.5. Examples of Finitely-Axiomatizable and Non-Finitely-Axiomatizable Multirelations -- 1.6. (k,p)-Interpretability -- 1.7. Homogeneous and Logically Homogeneous Multirelations -- 1.8. Rigid and Logically Rigid Multirelations -- Exercises -- 2/Logical Convergence; Compactness, Omission and Interpretability Theorems -- 2.1. Logical Convergence -- 2.2. Compactness Theorem -- 2.3. Omission Theorem -- 2.4. Interpretability Theorem -- 2.5. Every Injective Logical Operator is Invertible -- Exercise -- 3/Elimination of Quantifiers -- 3.1. Absolute Eliminant -- 3.2. (k,p)-Eliminant -- 3.3. Elimination Algorithms for the Chain of Rational Numbers and the Chain of Natural Numbers -- 3.4. Positive Dense Sum; Elimination of Quantifiers over the Sum of Rational or Real Numbers -- 3.5. Positive Discrete Divisible Sum; Elimination of Quantifiers over the Sum of Natural Numbers -- 3.6. Real Field; Elimination of Quantifiers over the Sum and Product of Algebraic Numbers or Real Numbers -- Exercises -- 4/Extension Theorems -- 4.1. Restrictive Sequence; (k,p)-Isomorphism and (k,p)-Identimorphism -- 4.2. Application to Logical Restriction -- 4.3. Projection Filter -- 4.4. Logical Extension Theorems -- 4.5. Theorem on Common Logical Extensions -- 4.6. Logical Morphism and Logical Embedding -- Exercises -- 5/Theories and Axiom Systems -- 5.1. Theory: Consistency; Intersection of Theories -- 5.1 Axiom System. Class of Models; Union-Theory, Finitely-Axiomatizable Theory, Saturated Theory -- 5.3. Complement of a Theory -- 5.4. Categoricity -- 5.5. Model-Saturated Theory -- Exercises -- 6/Pseudo-Logical Class; Interpretability of Theories; Expansion of a Theory; Axiomatizability -- 6.1. Pseudo-Logical Class -- 6.2. Interpretability of Theories -- 6.3. Canonical Expansion, Semantic Expansion, and Other Expansions -- 6.4. Axiomatizable Multirelations and Theories -- 6.5. Free Expansion -- Exercises -- 7/Ultraproduct -- 7.1. Family of Multirelations, Ultrafilter, Induced Logical Equivalence Class; Ultraproduct and Ultrapower; Maximal Case -- 7.2. Logical Equivalence Implies the Existence of Isomorphic Ultrapowers -- 7.3. Characterization of Logical Classes -- 7.4. Normal Ultraproduct; Definitions and Examples -- 7.5. Normal Ultraproducts and Logical Equivalence -- Exercises -- 8/Forcing -- 8.1. Generic Predicate; System: (+)-Forced and (?)-Forced Formulas -- 8.2. Elementary Properties -- 8.3. Forcing with Constraints -- 8.4. General Relation -- 8.5. Forcing and Deduction; Theory Forced by a Generic Predicate -- Exercises -- 9/Isomorphisms and Equivalences in Relation to the Calculus of Infinitely Long Formulas with Finite Quantifiers -- 9.1. ?-Isomorphism and ?-Equivalence -- 9.2. ?-Isomorphism and ?-Equivalence; Karpian Families -- 9.3. Automorphic Rank of a Multirelation -- 9.4. Multirelations with Denumerable Bases and ?-Isomorphisms -- 9.5. ?-Extension and ?-Interpretability -- 9.6. Infinite Logical Calculi and their Relation to Local Isomorphisms and Equivalences -- Proof of Lemmas Needed to Prove J. Robinsonโs Theorem -- Closure of a Relation -- References