Wikimedia Commons has media related to
Mathematical logic.

Mathematical logic has several meanings in common usage. It originally referred to symbolic or formal logic, and then came to be associated with the study of the logical (and even philosophical) foundations of mathematics. In contemporary use by mathematical logicians, the term refers to several branches of pure mathematics whose study involves careful attention to formal axiom systems and formal definability.

Mathematical logic is divided into four parts:

- Model theory
- Proof theory
- Recursion theory, also known as computability theory
- Set theory

The divisions between these areas, along with the divisions between mathematical logic and the rest of mathematics, are not completely sharp, with many areas of research and methods overlapping and reinforcing each other.

This category has the following 32 subcategories, out of 32 total.

- Forcing (mathematics) (23 P)
- Formal theories of arithmetic (17 P)

- Independence results (21 P)

- Quantifier (logic) (19 P)

- Substitution (logic) (3 P)

The following 200 pages are in this category, out of approximately 202 total. This list may not reflect recent changes.

(previous page) ( next page)- Cantor's paradox
- Cartesian monoid
- Categorical theory
- Class logic
- Classical mathematics
- Coherent space
- Cointerpretability
- Compactness theorem
- Complete theory
- Completeness (logic)
- Conservative extension
- Continuous predicate
- Contradiction
- Contraposition
- Converse relation
- Counting
- Craig interpolation
- Curry's paradox
- Cyclic negation

- Elementary definition
- Elementary equivalence
- Elementary sentence
- Elementary theory
- End extension
- Entitative graph
- Entscheidungsproblem
- Enumeration
- Enumeration reducibility
- Equality (mathematics)
- Equational logic
- Equiconsistency
- Extension by definitions
- Extension by new constant and function names
- Extensions of First Order Logic

- S2S (mathematics)
- Saturated model
- Schröder–Bernstein property
- Semantic theory of truth
- Semantics of logic
- Semicomputable function
- Signature (logic)
- Simplification of disjunctive antecedents
- Slicing the Truth
- Solèr's theorem
- Special case
- List of statements independent of ZFC
- Stratification (mathematics)
- Strength (mathematical logic)
- Structural induction
- Structuralism (philosophy of mathematics)
- Structure (mathematical logic)
- Subitizing
- Substructure (mathematics)
- Successor function
- Superposition calculus
- Surreal number
- Glossary of mathematical symbols
- List of mathematical symbols by subject