Category: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.
Wikimedia Commons has media related to: Mathematical logicSubcategories
This category has the following 24 subcategories, out of 24 total.
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B
C
D
F
F cont.
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L
M
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Pages in category "Mathematical logic"
The following 139 pages are in this category, out of 139 total. Updates to this list can occasionally be delayed for a few days.
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A
- Absoluteness (mathematical logic)
- Abstract algebraic logic
- Action algebra
- Additively indecomposable ordinal
- Algebraic logic
- Algorithm
- All horses are the same color (paradox)
- Ancestral relation
- Association for Symbolic Logic
- Attributional calculus
B
C
- Categorical set theory
- Classical mathematics
- Closure operator
- Coherent space
- Complete theory
- Computable model theory
- Computable real function
- Conservativity theorem
- Continuous predicate
- Contradiction
- Contraposition
- Craig interpolation
- Craig's theorem
- Curry's paradox
- Cyclic negation
D
E
- Entitative graph
- Entscheidungsproblem
- Enumeration
- Epsilon calculus
- Equiconsistency
- Erasure (logic)
- Extension by definitions
F
F cont.
G
- Game semantics
- Generalization (logic)
- Glivenko's theorem
- Gödel's completeness theorem
- Original proof of Gödel's completeness theorem
- Gödel's incompleteness theorems
- Ground expression
- Gödel number
H
- Herbrand base
- Herbrand structure
- Herbrand theory
- Herbrand universe
- Heyting algebra
- Hilbert's program
- Hypostatic abstraction
I
- Impredicativity
- Indicator function
- Inhabited set
- Institution (computer science)
- Institutional model theory
- Interior algebra
- Internal set
- Intuitionistic logic
- Inverse relation
K
L
- LF (logical framework)
- Laver table
- Laws of Form
- Leibniz operator
- Lindenbaum's lemma
- Lindenbaum–Tarski algebra
- List of basic topics in logic
- List of computability and complexity topics
- List of first-order theories
- Löb's theorem
- Logical graph
- Logical machine
- Ludics
- Łukasiewicz logic
M
M cont.
N
O
- Object theory
- On Formally Undecidable Propositions of Principia Mathematica and Related Systems
- Open sentence
- Operation (mathematics)
P
- Peirce's law
- Charles Sanders Peirce bibliography
- Predicate functor logic
- Principia Mathematica
- Proof of impossibility
- Proof sketch for Gödel's first incompleteness theorem
R
- Rational consequence relation
- Recursion
- Recursive definition
- Relation (mathematics)
- Relation algebra
- Residuated Boolean algebra
- Residuated lattice
- Reverse mathematics
- Rewriting
- Robinson's joint consistency theorem
- Rules of passage (logic)
S
- Set theory
- Smooth infinitesimal analysis
- Stratification (mathematics)
- Substitution instance
- Superposition calculus
- Surreal number
T
- T-schema
- Tarski's undefinability theorem
- Tautology (logic)
- Tennenbaum's theorem
- Turing's proof
- Turnstile (symbol)
- Two-element Boolean algebra
U
V
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