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