Algebraic methods of mathematical logic:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Prague [u.a.]
Academia
1967
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 200 - 206. - Aus d. Tschech. übers. |
| Beschreibung: | 210 S. |
Internformat
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| 245 | 1 | 0 | |a Algebraic methods of mathematical logic |c Ladislav Rieger. Czechoslov. Acad. of Sciences |
| 264 | 1 | |a Prague [u.a.] |b Academia |c 1967 | |
| 300 | |a 210 S. | ||
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| 650 | 4 | |a Boole, Algèbre de | |
| 650 | 4 | |a Logique symbolique et mathématique | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface
Contents
1. Introduction
1.1 Directions for the use of the introduction 9
1.2 A general characterization of mathematical logic 9
1.3 Formalization, mathematization, interpretation 10
1.4 The dialectic of the relation between mathematical and metamathematical aspects 12
1.5 Metamathematico mathematical parallelism and its natural limits 14
1.6 Practical applications of methods of mathematical logic 16
1.7 Principal mathematical tools of mathematical logic 17
1.8 Constructivism in metamathematics 18
1.9 Philosophy and mathematical logic 19
1.10 Methodological tasks and achievements of mathematical logic within mathematics 20
1.11 Semantics and pragmatics 22
1.12 Mathematical logic and logic in the broad sense 23
2. The language of mathematics and its symbolization
2.1 Mathematical logic and mathematical language as a material system of signs 25
2.2 The technique of symbolization of the language of mathematics 26
2.3 The substance and purpose of symbolization of mathematical language 30
2.4 Logical syntax and logical semantics 36
2.5 The idealized symbolical mathematical theory (without individual constants) and its
generalizations 36
3. Recursive construction of the relation of consequence
3.1 Fundamental descriptively syntactic rules 38
3.2 Fundamental descriptively semantic rules; definition of truth of a sentence 42
3.3 Recursive construction of the relation of consequence 48
3.4 Theorems on the relation of consequence; duality; the deduction theorem 54
4. Expressive possibilities of the present symbolization
4.1 Symbolic expression of operations and functions 70
4.2 Possibility of elementary symbolization of classical mathematics 72
7
Contents
4.3 Individual constants and their elimination 73
4.4 The syntactic approach to individual constants 78
4.5 Formalization of mathematical theories without primitive equality 80
5. Intuitive and mathematical notions of an idealized axiomatic mathematical theory
5.1 Critical annotations; arithmetization and algebraization 83
5.2 Logical frame of a language and mathematical theory 87
5.3 The algorithmic condition for a finite sequence of signs to be an expression; unique¬
ness of decomposition of expressions; the replacement theorem; scope of quantifica¬
tion 92
6. The algebraic theory of elementary predicate logic
6.1 The notion of Boolean algebra based on the order relation 101
6.2 The notion of Boolean algebra based on joins, meets and complementation 106
6.3 Basic algebraic tools of mathematical logic; Boolean subalgebras; homomorphisms;
ideals and prime ideals; set representation 112
7. Foundations of the algebraic theory of logical syntax
7.1 Free Boolean algebras, construction and representation 123
7.2 The algebraic aspect of propositional calculi 134
7.3 Algebraic properties of basic Lindenbaum algebras 140
7.3 Basic properties of joins and meets in Boolean algebras 143
7.5 Congruence of sentential expressions, renaming of bound individual indeterminates 146
7.6 Joins and meets in Lindenbaum algebras given by logical quantifiers; freedom of
basic Lindenbaum algebras 148
7.7 Indexed Boolean algebras 155
7.8 Homomorphisms and ideals in indexed Boolean algebras 164
7.9 Substitutive / ideals and formalized theories 172
7.10 Abstract characterization of Lindenbaum algebras 176
8. Algebraic laws of semantics of first order predicate logic
8.1 The relation of satisfaction; truth valuations; models of formalized theories 181
8.2 Algebraic characterization of basic semantical notions 186
8.3 Theorem on / prime over ideals for substitutively indexed algebras 189
8.4 Algebraic formulation of completeness of predicate logic 196
Bibliography 200
Index 207
8
|
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| spelling | Rieger, Ladislav 1916-1963 Verfasser (DE-588)140980199 aut Algebraic methods of mathematical logic Ladislav Rieger. Czechoslov. Acad. of Sciences Prague [u.a.] Academia 1967 210 S. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 200 - 206. - Aus d. Tschech. übers. Boole, Algèbre de Logique symbolique et mathématique Algebra, Boolean Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001256569&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rieger, Ladislav 1916-1963 Algebraic methods of mathematical logic Boole, Algèbre de Logique symbolique et mathématique Algebra, Boolean Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Algebraic methods of mathematical logic |
| title_auth | Algebraic methods of mathematical logic |
| title_exact_search | Algebraic methods of mathematical logic |
| title_full | Algebraic methods of mathematical logic Ladislav Rieger. Czechoslov. Acad. of Sciences |
| title_fullStr | Algebraic methods of mathematical logic Ladislav Rieger. Czechoslov. Acad. of Sciences |
| title_full_unstemmed | Algebraic methods of mathematical logic Ladislav Rieger. Czechoslov. Acad. of Sciences |
| title_short | Algebraic methods of mathematical logic |
| title_sort | algebraic methods of mathematical logic |
| topic | Boole, Algèbre de Logique symbolique et mathématique Algebra, Boolean Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Boole, Algèbre de Logique symbolique et mathématique Algebra, Boolean Logic, Symbolic and mathematical Mathematische Logik |
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