Mathematical logic is a field of mathematics that tries to formalize logic so that it can be used for mathematics more easily. Logic is about reasoning, and mathematical logic shows this with symbols. Most of mathematical logic was developed in the 19th and 20th century.
This field can be said to have four main sub-fields:
- set theory
- the study of mathematical proofs
- the study of recursion, and
- model theory
Related pages
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| General | |
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Theorems (list) & Paradoxes | |
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| Logics | | Traditional | |
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| Propositional | |
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| Predicate |
- First-order
- Second-order
- Higher-order
- Free
- Quantifiers
- Predicate
- Monadic predicate calculus
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| Set theory | | | Types of Sets |
- Countable
- Uncountable
- Empty
- Inhabited
- Singleton
- Finite
- Infinite
- Transitive
- Ultrafilter
- Recursive
- Fuzzy
- Universal
- Universe
- Constructible
- Grothendieck
- Von Neumann
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| Maps & Cardinality | |
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| Set theories |
- Zermelo–Fraenkel
- General
- Kripke–Platek
- Morse–Kelley
- Naive
- New Foundations
- Tarski–Grothendieck
- Von Neumann–Bernays–Gödel
- Ackermann
- Constructive
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Formal systems (list), Language & Syntax |
- Alphabet
- Arity
- Automata
- Axiom schema
- Expression
- Extension
- by definition
- Conservative
- Relation
- Formation rule
- Grammar
- Formula
- Atomic
- Closed
- Ground
- Open
- Free/bound variable
- Language
- Metalanguage
- Logical connective
- Predicate
- Functional
- Variable
- Propositional variable
- Proof
- Quantifier
- Sentence
- Signature
- String
- Substitution
- Symbol
- Function
- Logical/Constant
- Non-logical
- Variable
- Term
- Theory
| Example axiomatic systems (list) |
- of geometry:
- Euclidean:
- non-Euclidean* of arithmetic:
- Peano
- second-order
- elementary function
- primitive recursive
- Robinson
- Skolem
- of the real numbers
- of Boolean algebras
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| Proof theory | |
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| Model theory |
- Truth value
- Interpretation
- Model
- Equivalence
- Finite
- Saturated
- Spectrum
- Submodel
- Non-standard model
- Diagram
- Categorical theory
- Model complete theory
- Satisfiability
- Semantics of logic
- Strength
- Theories of truth
- Semantic
- Tarski's
- Kripke's
- T-schema
- Transfer principle
- Truth predicate
- Type
- Ultraproduct
- Validity
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| Computability theory | |
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| Related | |
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