Algebraic methods of mathematical logic
Algebraic Methods of Mathematical Logic.
| Main Author: | Rieger, Ladislav, 1916-1963. |
|---|---|
| Other Authors: | ScienceDirect (Online service) |
| Format: | eBook |
| Language: | English Undetermined |
| Published: |
Prague : New York :
Academia; Academic Press,
1967.
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| Physical Description: |
1 online resource (210 pages) |
| Subjects: |
Table of Contents:
- Front Cover; Algebraic Methods of Mathematical Logic; Copyright Page; Preface; ERRATA; Table ofContents; Chapter 1.INTRODUCTION; 1.1. Directions for the use of the introduction; 1.2. A general characterization of mathematical logic; 1.3. Formalization, mathematization, interpretation; 1.4. The dialectic of the relation between mathematical and metamathematical aspects; 1.5. Metamathematico-mathematical parallelism and its natural limits; 1.6. Practical applications of methods of mathematical logic; 1.7. Principal mathematical tools of mathematical logic; 1.8. Constructivism in metamathematics.
- 1.9. Philosophy and mathematical logic1.10. Methodological tasks and achievements of mathematical logic within mathematics; 1.11. Semantics and pragmatics; 1.12. Mathematical logic and logic in the broad sense; Chapter 2. THE LANGUAGE OF MATHEMATICS AND ITS SYMBOLIZATION; 2.1. Mathematical logic and mathematical language as a material system of signs; 2.2. The technique of symbolization of the language of mathematics; 2.3. The substance and purpose of symbolization of mathematical language; 2.4. Logical syntax and logical semantics.
- 2.5. The idealized symbolical mathematical theory (without individual constants) and its generalizationsChapter 3. RECURSIVE CONSTRUCTION OF THE RELATION OF CONSEQUENCE; 3.1. Fundamental descriptively-syntactic rules; 3.2. Fundamental descriptively-semantic rules; definition of truth of a sentence; 3.3. Recursive construction of the relation of consequence; 3.4. Theorems on the relation of consequence; duality; the deduction theorem; Chapter 4. EXPRESSIVE POSSIBILITIES OF THE PRESENT SYMBOLIZATION; 4.1. Symbolic expression of operations and functions.
- 4.2. Possibility of elementary symbolization of classical mathematics4.3. Individual constants and their elimination; 4.4. The syntactic approach to individual constants; 4.5. Formalization of mathematical theories without primitive equality; Chapter 5. INTUITIVE AND MATHEMATICAL NOTIONS OF AN IDEALIZED AXIOMATIC MATHEMATICAL THEORY; 5.1. Critical annotations; arithmetization and algebraization; 5.2. Logical frame of a language and mathematical theory; 5.3. The algorithmic condition for a finite sequence of signs to be an expression; uniqueness of decomposition of expressions.
- The replacement theorem scope of quantification; Chapter 6. THE ALGEBRAIC THEORY OF ELEMENTARY PREDICATE LOGIC; 6.1. The notion of Boolean algebra based on the order relation; 6.2. The notion of Boolean algebra based on joins, meets and complementation; 6.3. Basic algebraic tools of mathematical logic; Boolean subalgebras; homomorphisms; ideals and prime ideals; set representation; Chapter 7. FOUNDATIONS OF THE ALGEBRAIC THEORY OF LOGICAL SYNTAX; 7.1. Free Boolean algebras, construction and representation; 7.2. The algebraic aspect of propositional calculi.