Mathematical logic. ([2018?])
- Record Type:
- Book
- Title:
- Mathematical logic. ([2018?])
- Main Title:
- Mathematical logic
- Further Information:
- Note: By Joseph R. Shoenfield.
- Authors:
- Shoenfield, Joseph R (Joseph Robert), 1927-
- Contents:
- Cover -- Title Page -- Copyright Page -- PREFACE -- Table of Contents -- Dedication -- Chapter 1: The Nature of Mathematical Logic -- 1.1 Axiom systems -- 1.2 Formal systems -- 1.3 Syntactical variables -- Chapter 2: First-Order Theories -- 2.1 Functions and predicates -- 2.2 Truth functions -- 2.3 Variables and quantifiers -- 2.4 First-order languages -- 2.6 Logical axioms and rules -- 2.5 Structures -- Problems -- Chapter 3: Theorems in First-Order Theories -- 3.1 The tautology theorem -- 3.2 Results on quantifiers -- 3.3 The deduction theorem -- 3.4 The equivalence and equality theorems -- 3.5 Prenex form -- Problems -- Chapter 4: The Characterization Problem -- 4.1 The reduction theorem -- 4.2 The completeness theorem -- 4.3 The consistency theorem -- 4.4 Herbrand's theorem -- 4.5 Addition of function symbols -- 4.6 Extensions by definitions -- 4.7 Interpretations -- Problems -- Chapter 5: The Theory of Models -- 5.1 The compactness theorem -- 5.2 Isomorphisms and substructures -- 5.3 Cardinality of models -- 5.4 Joint consistency -- 5.5 Complete theories -- 5.6 Categoricity -- Problems -- Chapter 6: Incompleteness and Undecidability -- 6.1 Calculability -- 6.2 Recursive functions -- 6.3 Explicit definitions -- 6.4 Sequence numbers -- 6.5 Church's thesis -- 6.6 Expression numbers -- 6.7 Representability -- 6.8 Church's theorem and the incompleteness theorem -- 6.9 Undecidability -- Chapter 7: Recursion Theory -- 7.1 Partial functions -- 7.2 Functionals and relations --Cover -- Title Page -- Copyright Page -- PREFACE -- Table of Contents -- Dedication -- Chapter 1: The Nature of Mathematical Logic -- 1.1 Axiom systems -- 1.2 Formal systems -- 1.3 Syntactical variables -- Chapter 2: First-Order Theories -- 2.1 Functions and predicates -- 2.2 Truth functions -- 2.3 Variables and quantifiers -- 2.4 First-order languages -- 2.6 Logical axioms and rules -- 2.5 Structures -- Problems -- Chapter 3: Theorems in First-Order Theories -- 3.1 The tautology theorem -- 3.2 Results on quantifiers -- 3.3 The deduction theorem -- 3.4 The equivalence and equality theorems -- 3.5 Prenex form -- Problems -- Chapter 4: The Characterization Problem -- 4.1 The reduction theorem -- 4.2 The completeness theorem -- 4.3 The consistency theorem -- 4.4 Herbrand's theorem -- 4.5 Addition of function symbols -- 4.6 Extensions by definitions -- 4.7 Interpretations -- Problems -- Chapter 5: The Theory of Models -- 5.1 The compactness theorem -- 5.2 Isomorphisms and substructures -- 5.3 Cardinality of models -- 5.4 Joint consistency -- 5.5 Complete theories -- 5.6 Categoricity -- Problems -- Chapter 6: Incompleteness and Undecidability -- 6.1 Calculability -- 6.2 Recursive functions -- 6.3 Explicit definitions -- 6.4 Sequence numbers -- 6.5 Church's thesis -- 6.6 Expression numbers -- 6.7 Representability -- 6.8 Church's theorem and the incompleteness theorem -- 6.9 Undecidability -- Chapter 7: Recursion Theory -- 7.1 Partial functions -- 7.2 Functionals and relations -- 7.3 Properties of recursive functionals -- 7.4 Indices -- 7.5 The arithmetical hierarchy -- 7.6 Relative recursiveness -- 7.7 Degrees -- 7.8 The analytical hierarchy -- 7.9 Hyperarithmetical relations -- 7.10 The characterization theorem -- 7.11 Basis theorems -- Problems -- Chapter 8: The Natural Numbers -- 8.1 Peano arithmetic -- 8.2 The theorem on consistency proofs. 8.3 The consistency proof -- 8.4 Applications of the consistency proof -- 8.5 Second-order arithmetic -- Problems -- Chapter 9: Set Theory -- 9.1 Axioms for sets -- 9.2 Development of set theory -- 9.3 Ordinals -- 9.4 Cardinals -- 9.5 Interpretations of set theory -- 9.6 Constructible sets -- 9.7 The axiom of constructibility -- 9.8 Forcing -- 9.9 The independence proofs -- 9.10 Large cardinals -- Problems -- Appendix The Word Problem -- Index. … (more)
- Publisher Details:
- Boca Raton : CRC Press
- Publication Date:
- 2018
- Copyright Date:
- 1967
- Extent:
- 1 online resource
- Subjects:
- 511.3
Logic, Symbolic and mathematical
Electronic books - Languages:
- English
- ISBNs:
- 9781351433303
- Related ISBNs:
- 135143330X
9781568811352
1568811357 - Access Rights:
- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
- Access Usage:
- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.282039
- Ingest File:
- 02_327.xml