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.
|
| Physical Description: |
1 online resource (210 pages) |
| Subjects: |
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| 003 | OCoLC | ||
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| 100 | 1 | |a Rieger, Ladislav, |d 1916-1963. | |
| 245 | 1 | 0 | |a Algebraic methods of mathematical logic / |c Translated by Michael Basch. |
| 264 | 1 | |a Prague : |b Academia; |a New York : |b Academic Press, |c 1967. | |
| 300 | |a 1 online resource (210 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
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| 504 | |a Includes bibliographical references (pages 200-206). | ||
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| 533 | |a Electronic reproduction. |b [S.l.] : |c HathiTrust Digital Library, |d 2010. |5 MiAaHDL. | ||
| 538 | |a Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |u http://purl.oclc.org/DLF/benchrepro0212 |5 MiAaHDL. | ||
| 583 | 1 | |a digitized |c 2010 |h HathiTrust Digital Library |l committed to preserve |2 pda |5 MiAaHDL. | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a Algebraic Methods of Mathematical Logic. | ||
| 650 | 0 | |a Logic, Symbolic and mathematical. | |
| 650 | 0 | |a Algebra, Boolean. | |
| 650 | 6 | |a Logique symbolique et mathématique. | |
| 650 | 6 | |a Boole, Algèbre de. | |
| 650 | 7 | |a MATHEMATICS |x Logic. |2 bisacsh. | |
| 650 | 7 | |a Algebra, Boolean. |2 fast. | |
| 650 | 7 | |a Logic, Symbolic and mathematical. |2 fast. | |
| 650 | 0 | 7 | |a Mathematische Logik. |2 swd. |
| 655 | 4 | |a Electronic books. | |
| 710 | 2 | |a ScienceDirect (Online service) | |
| 776 | 0 | 8 | |i Print version: |a Rieger, Ladislav, 1916-1963. |t Algebraic methods of mathematical logic. |d Prague, Academia; New York, Academic Press, 1967 |w (DLC) 66027810 |w (OCoLC)2655859. |
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