Mathematical logic and foundations
- General reference works (handbooks, dictionaries, bibliographies, etc.)
- Instructional exposition (textbooks, tutorial papers, etc.)
- Research exposition (monographs, survey articles)
- Historical (must also be assigned at least one classification number from Section 01)
- Explicit machine computation and programs (not the theory of computation or programming)
- Proceedings, conferences, collections, etc.
- Philosophical and critical
- General logic
- Classical propositional logic
- Classical first-order logic
- Higher-order logic and type theory
- Subsystems of classical logic (including intuitionistic logic)
- Abstract deductive systems
- Decidability of theories and sets of sentences
- Foundations of classical theories (including reverse mathematics)
- Mechanization of proofs and logical operations
- Combinatory logic and lambda-calculus
- Logic of knowledge and belief
- Temporal logic
- Modal logic
- Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
- Probability and inductive logic
- Many-valued logic
- Fuzzy logic; logic of vagueness
- Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)
- Intermediate logics
- Other nonclassical logic
- Logic of natural languages
- Logic in computer science
- Other applications of logic
- None of the above, but in this section
- Model theory
- Equational classes, universal algebra
- Basic properties of first-order languages and structures
- Quantifier elimination, model completeness and related topics
- Finite structures
- Denumerable structures
- Ultraproducts and related constructions
- Model-theoretic forcing
- Other model constructions
- Categoricity and completeness of theories
- Interpolation, preservation, definability
- Classification theory, stability and related concepts
- Models with special properties (saturated, rigid, etc.)
- Properties of classes of models
- Set-theoretic model theory
- Effective and recursion-theoretic model theory
- Model-theoretic algebra
- Models of arithmetic and set theory
- Model theory of ordered structures; o-minimality
- Models of other mathematical theories
- Other classical first-order model theory
- Logic on admissible sets
- Other infinitary logic
- Logic with extra quantifiers and operators
- Second- and higher-order model theory
- Nonclassical models (Boolean-valued, sheaf, etc.)
- Abstract model theory
- Applications of model theory
- None of the above, but in this section
- Computability and recursion theory
- Thue and Post systems, etc.
- Automata and formal grammars in connection with logical questions
- Turing machines and related notions
- Complexity of computation
- Recursive functions and relations, subrecursive hierarchies
- Recursively (computably) enumerable sets and degrees
- Other Turing degree structures
- Other degrees and reducibilities
- Undecidability and degrees of sets of sentences
- Word problems, etc.
- Theory of numerations, effectively presented structures
- Recursive equivalence types of sets and structures, isols
- Hierarchies
- Computability and recursion theory on ordinals, admissible sets, etc.
- Higher-type and set recursion theory
- Inductive definability
- Abstract and axiomatic computability and recursion theory
- Applications of computability and recursion theory
- None of the above, but in this section
- Set theory
- Partition relations
- Ordered sets and their cofinalities; pcf theory
- Other combinatorial set theory
- Ordinal and cardinal numbers
- Descriptive set theory
- Cardinal characteristics of the continuum
- Other classical set theory (including functions, relations, and set algebra)
- Axiom of choice and related propositions
- Axiomatics of classical set theory and its fragments
- Consistency and independence results
- Other aspects of forcing and Boolean-valued models
- Inner models, including constructibility, ordinal definability, and core models
- Other notions of set-theoretic definability
- Continuum hypothesis and Martin's axiom
- Large cardinals
- Determinacy principles
- Other hypotheses and axioms
- Nonclassical and second-order set theories
- Fuzzy set theory
- Applications of set theory
- None of the above, but in this section
- Proof theory and constructive mathematics
- Proof theory, general
- Cut-elimination and normal-form theorems
- Structure of proofs
- Functionals in proof theory
- Recursive ordinals and ordinal notations
- Complexity of proofs
- Relative consistency and interpretations
- First-order arithmetic and fragments
- Second- and higher-order arithmetic and fragments
- Gödel numberings in proof theory
- Provability logics and related algebras (e.g., diagonalizable algebras)
- Metamathematics of constructive systems
- Linear logic and other substructural logics
- Intuitionistic mathematics
- Constructive and recursive analysis
- Other constructive mathematics
- None of the above, but in this section
- Algebraic logic
- Boolean algebras
- Lattices and related structures
- Quantum logic
- Cylindric and polyadic algebras; relation algebras
- Lukasiewicz and Post algebras
- Other algebras related to logic
- Categorical logic, topoi
- None of the above, but in this section
- Nonstandard models
- Nonstandard models in mathematics
- Other applications of nonstandard models (economics, physics, etc.)
- Nonstandard models of arithmetic
- None of the above, but in this section
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