Biblioteca Dr. Antonio Monteiro · Catálogo | |
03 | Mathematical logic and foundations | ||
03-00 | General reference works (handbooks, dictionaries, bibliographies, etc.) | ||
03-01 | Instructional exposition (textbooks, tutorial papers, etc.) | ||
03-02 | Research exposition (monographs, survey articles) | ||
03-03 | Historical | ||
03-04 | Explicit machine computation and programs (not the theory of computation or programming) | ||
03-06 | Proceedings, conferences, collections, etc. | ||
03-99 | Mathematical logic and foundations (not classified at a more specific level) | ||
03A05 | Philosophical and critical {For philosophy of mathematics, see also 00A30} | ||
03B | General logic | ||
03B05 | Classical propositional logic | ||
03B10 | Classical first-order logic | ||
03B15 | Higher-order logic and type theory | ||
03B20 | Subsystems of classical logic (including intuitionistic logic) | ||
03B22 | Abstract deductive systems | ||
03B25 | Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10] | ||
03B30 | Foundations of classical theories (including reverse mathematics) [See also 03F35] | ||
03B35 | Mechanization of proofs and logical operations [See also 68T15] | ||
03B40 | Combinatory logic and lambda-calculus [See also 68N18] | ||
03B42 | Logic of knowledge and belief | ||
03B44 | Temporal logic | ||
03B45 | Modal logic {For knowledge and belief see 03B42; for temporal logic see 03B44; for provability logic see also 03F45} | ||
03B47 | Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52} | ||
03B48 | Probability and inductive logic [See also 60A05] | ||
03B50 | Many-valued logic | ||
03B52 | Fuzzy logic; logic of vagueness [See also 68T27, 68T37, 94D05] | ||
03B53 | Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.) | ||
03B55 | Intermediate logics | ||
03B60 | Other nonclassical logic | ||
03B65 | Logic of natural languages [See also 68T50, 91F20] | ||
03B70 | Logic in computer science [See also 68-XX] | ||
03B80 | Other applications of logic | ||
03B99 | None of the above, but in this section | ||
03C | Model theory | ||
03C05 | Equational classes, universal algebra [See also 08Axx, 08Bxx, 18C05] | ||
03C07 | Basic properties of first-order languages and structures | ||
03C10 | Quantifier elimination, model completeness and related topics | ||
03C13 | Finite structures [See also 68Q15, 68Q19] | ||
03C15 | Denumerable structures | ||
03C20 | Ultraproducts and related constructions | ||
03C25 | Model-theoretic forcing | ||
03C30 | Other model constructions | ||
03C35 | Categoricity and completeness of theories | ||
03C40 | Interpolation, preservation, definability | ||
03C45 | Classification theory, stability and related concepts | ||
03C50 | Models with special properties (saturated, rigid, etc.) | ||
03C52 | Properties of classes of models | ||
03C55 | Set-theoretic model theory | ||
03C57 | Effective and recursion-theoretic model theory [See also 03D45] | ||
03C60 | Model-theoretic algebra [See also 08C10, 12Lxx, 13L05] | ||
03C62 | Models of arithmetic and set theory [See also 03Hxx] | ||
03C64 | Model theory of ordered structures; o-minimality | ||
03C65 | Models of other mathematical theories | ||
03C68 | Other classical first-order model theory | ||
03C70 | Logic on admissible sets | ||
03C75 | Other infinitary logic | ||
03C80 | Logic with extra quantifiers and operators [See also 03B42, 03B44, 03B45, 03B48] | ||
03C85 | Second- and higher-order model theory | ||
03C90 | Nonclassical models (Boolean-valued, sheaf, etc.) | ||
03C95 | Abstract model theory | ||
03C98 | Applications of model theory [See also 03C60] | ||
03C99 | None of the above, but in this section | ||
03D | Computability and recursion theory | ||
03D03 | Thue and Post systems, etc. | ||
03D05 | Automata and formal grammars in connection with logical questions [See also 68Q45, 68Q70, 68R15] | ||
03D10 | Turing machines and related notions [See also 68Q05] | ||
03D15 | Complexity of computation [See also 68Q15, 68Q17] | ||
03D20 | Recursive functions and relations, subrecursive hierarchies | ||
03D25 | Recursively (computably) enumerable sets and degrees | ||
03D28 | Other Turing degree structures | ||
03D30 | Other degrees and reducibilities | ||
03D35 | Undecidability and degrees of sets of sentences | ||
03D40 | Word problems, etc. [See also 06B25, 08A50, 20F10, 68R15] | ||
03D45 | Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55] | ||
03D50 | Recursive equivalence types of sets and structures, isols | ||
03D55 | Hierarchies | ||
03D60 | Computability and recursion theory on ordinals, admissible sets, etc. | ||
03D65 | Higher-type and set recursion theory | ||
03D70 | Inductive definability | ||
03D75 | Abstract and axiomatic computability and recursion theory | ||
03D80 | Applications of computability and recursion theory | ||
03D99 | None of the above, but in this section | ||
03E | Set theory | ||
03E02 | Partition relations | ||
03E04 | Ordered sets and their cofinalities; pcf theory | ||
03E05 | Other combinatorial set theory | ||
03E10 | Ordinal and cardinal numbers | ||
03E15 | Descriptive set theory [See also 28A05, 54H05] | ||
03E17 | Cardinal characteristics of the continuum | ||
03E20 | Other classical set theory (including functions, relations, and set algebra) | ||
03E25 | Axiom of choice and related propositions | ||
03E30 | Axiomatics of classical set theory and its fragments | ||
03E35 | Consistency and independence results | ||
03E40 | Other aspects of forcing and Boolean-valued models | ||
03E45 | Inner models, including constructibility, ordinal definability, and core models | ||
03E47 | Other notions of set-theoretic definability | ||
03E50 | Continuum hypothesis and Martin's axiom | ||
03E55 | Large cardinals | ||
03E60 | Determinacy principles | ||
03E65 | Other hypotheses and axioms | ||
03E70 | Nonclassical and second-order set theories | ||
03E72 | Fuzzy set theory | ||
03E75 | Applications of set theory | ||
03E99 | None of the above, but in this section | ||
03F | Proof theory and constructive mathematics | ||
03F03 | Proof theory, general | ||
03F05 | Cut-elimination and normal-form theorems | ||
03F07 | Structure of proofs | ||
03F10 | Functionals in proof theory | ||
03F15 | Recursive ordinals and ordinal notations | ||
03F20 | Complexity of proofs | ||
03F25 | Relative consistency and interpretations | ||
03F30 | First-order arithmetic and fragments | ||
03F35 | Second- and higher-order arithmetic and fragments [See also 03B30] | ||
03F40 | Gödel numberings in proof theory | ||
03F45 | Provability logics and related algebras (e.g., diagonalizable algebras) [See also 03B45, 03G25, 06E25] | ||
03F50 | Metamathematics of constructive systems | ||
03F52 | Linear logic and other substructural logics [See also 03B47] | ||
03F55 | Intuitionistic mathematics | ||
03F60 | Constructive and recursive analysis [See also 03B30, 03D45, 26E40, 46S30, 47S30] | ||
03F65 | Other constructive mathematics [See also 03D45] | ||
03F99 | None of the above, but in this section | ||
03G | Algebraic logic | ||
03G05 | Boolean algebras [See also 06Exx] | ||
03G10 | Lattices and related structures [See also 06Bxx] | ||
03G12 | Quantum logic [See also 06C15, 81P10] | ||
03G15 | Cylindric and polyadic algebras; relation algebras | ||
03G20 | Lukasiewicz and Post algebras [See also 06D25, 06D30] | ||
03G25 | Other algebras related to logic [See also 03F45, 06D20, 06E25, 06F35] | ||
03G30 | Categorical logic, topoi [See also 18B25, 18C05, 18C10] | ||
03G99 | None of the above, but in this section | ||
03H | Nonstandard models [See also 03C62] | ||
03H05 | Nonstandard models in mathematics [See also 26E35, 28E05, 30G06, 46S20, 47S20, 54J05] | ||
03H10 | Other applications of nonstandard models (economics, physics, etc.) | ||
03H15 | Nonstandard models of arithmetic [See also 11U10, 12L15, 13L05] | ||
03H99 | None of the above, but in this section |
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