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Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Foundations, logic, and set theory

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This page lists articles that have been assigned to the field Foundations, logic, and set theory using the {{maths rating}} template. To include articles on this page, use the following wiki code (in which newlines are optional).

{{maths rating
  |class = quality grading (FA, A, GA, Bplus, B, Start, or Stub)
  |importance = priority level (Top, High, Mid, or Low)
  |field = Foundations
}}

Description

This field is for articles which on foundational aspects of mathematics, including:

mathematical logic, model theory, set theory, some general topology and category theory.

Some articles in these areas might instead be rated under algebra or topology, depending on their content. This field does not include articles on elementary set theory or arithmetic, which are rated under basics.

Foundations, logic, and set theory article ratings
Priority Quality
Featured article FA A-Class article A Good article GA A-BB+ B Start Stub UA Total
Top 0 0 0 3 11 5 0 0 19
High 0 0 0 3 21 35 4 0 63
Mid 0 1 0 7 41 88 44 0 181
Low 0 0 0 1 15 79 100 0 195
UA 0 0 0 0 0 1 0 1 2
Total 0 1 0 14 88 208 148 1 460
Last updated: Sun Jul 5 01:10:02 UTC 2009

The articles in this field are sorted by importance (or priority) and listed in the tables below. These tables are updated automatically by VeblenBot.

Foundations, logic, and set theory articles by priority
Top-Priority High-Priority Mid-Priority Low-Priority Unassessed priority

Top-Priority

Article Grade Comments
  Category theory (talk) A-BB+
  Logic (talk) A-BB+
  Mathematical induction (talk) A-BB+
  Axiom of choice (talk) B
  Boolean algebra (logic) (talk) B
  Category (mathematics) (talk) B
  Computable function (talk) B
  Equivalence relation (talk) B
  Gödel's incompleteness theorems (talk) B
  Mathematical logic (talk) B
  Propositional calculus (talk) B
  Russell's paradox (talk) B
  Set (mathematics) (talk) B
  Set theory (talk) B
  Commutative diagram (talk) Start
  Conjecture (talk) Start
  Foundations of mathematics (talk) Start
  Function composition (talk) Start
  Mathematical proof (talk) Start
Last updated: Sun Jul 5 01:10:02 UTC 2009

High-Priority

Article Grade Comments
  Constructible universe (talk) A-BB+
  Fibred category (talk) A-BB+
  Turing machine (talk) A-BB+
  Adjoint functors (talk) B
  Axiomatic set theory (talk) B
  Cantor's diagonal argument (talk) B
  Cantor's theorem (talk) B
  Cardinal number (talk) B
  Cardinality of the continuum (talk) B
  Cofinality (talk) B
  Complete lattice (talk) B
  Continuum hypothesis (talk) B
  Epimorphism (talk) B
  First-order logic (talk) B
  Functor (talk) B
  Hom functor (talk) B
  Inverse function (talk) B
  Lattice (order) (talk) B
  Löwenheim–Skolem theorem (talk) B
  Morphism (talk) B
  Ordinal number (talk) B
  Proof theory (talk) B
  Structure (mathematical logic) (talk) B
  Well-order (talk) B
  Aleph number (talk) Start
  Axiom (talk) Start
  Bijection (talk) Start
  Cardinality (talk) Start
  Cartesian closed category (talk) Start
  Church–Turing thesis (talk) Start
  Closure (mathematics) (talk) Start
  Complete category (talk) Start
  Completeness (talk) Start
  Countable set (talk) Start
  Descriptive set theory (talk) Start
  Determinacy (talk) Start
  Equality (mathematics) (talk) Start
  Equivalence class (talk) Start
  Finitary relation (talk) Start
  Gödel number (talk) Start
  Indicator function (talk) Start
  Intersection (set theory) (talk) Start
  Intuitionistic logic (talk) Start
  Kleene's recursion theorem (talk) Start
  Large cardinal property (talk) Start
  Logical conjunction (talk) Start
  Metamathematics (talk) Start
  Naive set theory (talk) Start
  Natural transformation (talk) Start
  Negation (talk) Start
  Partially ordered set (talk) Start
  Partition of a set (talk) Start
  Set-builder notation (talk) Start
  Subset (talk) Start
  Topos (talk) Start
  Transfinite induction (talk) Start
  Universal property (talk) Start
  Zermelo–Fraenkel set theory (talk) Start
  Zorn's lemma (talk) Start
  Formal proof (talk) Stub
  Power set (talk) Stub
  Set-theoretic topology (talk) Stub
  Soundness (talk) Stub
Last updated: Sun Jul 5 01:10:02 UTC 2009

Mid-Priority

Article Grade Comments
  Peano axioms (talk) A-Class article A
  Allegory (category theory) (talk) A-BB+
  Boolean algebra (structure) (talk) A-BB+
  Implementation of mathematics in set theory (talk) A-BB+
  Kolmogorov complexity (talk) A-BB+
  Method of analytic tableaux (talk) A-BB+
  Second-order logic (talk) A-BB+
  Turing degree (talk) A-BB+
  Abelian category (talk) B
  Analytical hierarchy (talk) B
  Arithmetical hierarchy (talk) B
  Axiom schema of replacement (talk) B
  Banach–Tarski paradox (talk) B
  Binary relation (talk) B
  Borel hierarchy (talk) B
  Busy beaver (talk) B
  Cantor's paradox (talk) B
  Combinatory logic (talk) B
  Concrete category (talk) B
  Decidability (logic) (talk) B
  Exact category (talk) B
  Forcing (mathematics) (talk) B
  Hilbert's tenth problem (talk) B
  Kripke semantics (talk) B
  Lambda calculus (talk) B
  Large countable ordinal (talk) B
  Natural deduction (talk) B
  New Foundations (talk) B
  Paraconsistent logic (talk) B
  Paradoxes of set theory (talk) B
  Prenex normal form (talk) B
  Primitive recursive function (talk) B
  Prisoner's dilemma (talk) B
  Quantification (talk) B
  Recursion (talk) B
  Recursion theory (talk) B
  Register machine (talk) B
  Reverse mathematics (talk) B
  Second-order arithmetic (talk) B
  Sequent calculus (talk) B
  Skolem's paradox (talk) B
  Tarski's undefinability theorem (talk) B
  Tautology (logic) (talk) B
  Total order (talk) B
  Type (model theory) (talk) B
  Venn diagram (talk) B
  Zermelo set theory (talk) B
  Μ operator (talk) B
  Μ-recursive function (talk) B
  Absolute presentation of a group (talk) Start
  Analytic set (talk) Start
  Arbitrary-precision arithmetic (talk) Start
  Arithmetical set (talk) Start
  Assignment (mathematical logic) (talk) Start
  Atomic sentence (talk) Start
  Automorphism (talk) Start
  Axiom of determinacy (talk) Start
  Axiom of extensionality (talk) Start
  Axiom of power set (talk) Start
  Axiomatic system (talk) Start
  Baire category theorem (talk) Start
  Baire space (set theory) (talk) Start
  Banach–Mazur game (talk) Start
  Binary operation (talk) Start
  Boolean-valued function (talk) Start
  Borel set (talk) Start
  Bounded quantifier (talk) Start
  Cantor–Bernstein–Schroeder theorem (talk) Start
  Cartesian product (talk) Start
  Categorical logic (talk) Start
  Category of sets (talk) Start
  Compactness theorem (talk) Start
  Computable number (talk) Start
  Consistency (talk) Start
  Constructivism (mathematics) (talk) Start
  Curry–Howard correspondence (talk) Start
  De Morgan's laws (talk) Start
  Deduction theorem (talk) Start
  Definable set (talk) Start
  Derived functor (talk) Start
  Direct limit (talk) Start
  Direct product (talk) Start
  Directed set (talk) Start
  Dual (category theory) (talk) Start
  Elementary class (talk) Start
  Embedding (talk) Start
  Empty set (talk) Start
  Finite model theory (talk) Start
  Finite set (talk) Start
  Formal system (talk) Start
  Frege's propositional calculus (talk) Start
  Grothendieck topology (talk) Start
  Gödel's completeness theorem (talk) Start
  Hilbert's paradox of the Grand Hotel (talk) Start
  Identifiability condition (talk) Start
  If and only if (talk) Start
  Image (mathematics) (talk) Start
  Informal logic (talk) Start
  Injective function (talk) Start
  Injective object (talk) Start
  Inner model theory (talk) Start
  Interpretation (logic) (talk) Start
  Intuitionism (talk) Start
  Invalid proof (talk) Start
  Kan extension (talk) Start
  Kernel (category theory) (talk) Start
  Kripke–Platek set theory (talk) Start
  König's theorem (set theory) (talk) Start
  Logical disjunction (talk) Start
  Measurable cardinal (talk) Start
  Model theory (talk) Start
  Monoidal category (talk) Start
  Monomorphism (talk) Start
  Multiset (talk) Start
  Ordered pair (talk) Start
  Ordinal analysis (talk) Start
  Post's theorem (talk) Start
  Predicate (mathematical logic) (talk) Start
  Predicate variable (talk) Start
  Product (category theory) (talk) Start
  Projective object (talk) Start
  Proof without words (talk) Start
  Propositional formula (talk) Start
  Pseudoelementary class (talk) Start
  Quotient category (talk) Start
  Set notation (talk) Start
  Soundness theorem (talk) Start
  Transitive relation (talk) Start
  Truth table (talk) Start
  Type theory (talk) Start
  Undecidable problem (talk) Start
  Union (set theory) (talk) Start
  Units place (talk) Start
  Universe (mathematics) (talk) Start
  Von Neumann universe (talk) Start
  Well-founded relation (talk) Start
  Yoneda lemma (talk) Start
  Aczel's anti-foundation axiom (talk) Stub
  Algebraic logic (talk) Stub
  Axiom of countable choice (talk) Stub
  Axiom of dependent choice (talk) Stub
  Axiom schema (talk) Stub
  Borel equivalence relation (talk) Stub
  Braided monoidal category (talk) Stub
  Choice function (talk) Stub
  Class (set theory) (talk) Stub
  Closed monoidal category (talk) Stub
  Complete Boolean algebra (talk) Stub
  Composition operator (talk) Stub
  Contradiction (talk) Stub
  Cut-elimination theorem (talk) Stub
  Deductive system (talk) Stub
  Descent (category theory) (talk) Stub
  Descriptive interpretation (talk) Stub
  Diagram (category theory) (talk) Stub
  Disjoint sets (talk) Stub
  Disjoint union (talk) Stub
  Element (mathematics) (talk) Stub
  Expression (mathematics) (talk) Stub
  Formation rule (talk) Stub
  Formula (mathematical logic) (talk) Stub
  Free variables and bound variables (talk) Stub
  Generic filter (talk) Stub
  Hereditary set (talk) Stub
  Independence (mathematical logic) (talk) Stub
  Indiscernibles (talk) Stub
  Initial and terminal objects (talk) Stub
  Kernel (set theory) (talk) Stub
  L(R) (talk) Stub
  Limitation of size (talk) Stub
  Projective hierarchy (talk) Stub
  Proof calculus (talk) Stub
  Proof procedure (talk) Stub
  Propositional variable (talk) Stub
  Recursive definition (talk) Stub
  Sentence (mathematical logic) (talk) Stub
  Subobject (talk) Stub
  Typed lambda calculus (talk) Stub
  Well-defined (talk) Stub
  Well-formed formula (talk) Stub
  Well-ordering theorem (talk) Stub
Last updated: Sun Jul 5 01:10:02 UTC 2009

Low-Priority

Article Grade Comments
  Ackermann function (talk) A-BB+
  Algorithm characterizations (talk) B
  Arrow's impossibility theorem (talk) B
  Axiom of pairing (talk) B
  Axiom of regularity (talk) B
  Axiom schema of specification (talk) B
  Borel determinacy theorem (talk) B
  Bridge and torch problem (talk) B
  Cantor's first uncountability proof (talk) B
  Functional completeness (talk) B
  Non-standard analysis (talk) B
  Post–Turing machine (talk) B
  Signature (logic) (talk) B
  Triangulated category (talk) B
  Turing reduction (talk) B
  Turing's proof (talk) B
  Abstract algebraic logic (talk) Start
  Ackermann set theory (talk) Start
  Additive category (talk) Start
  Algorithm examples (talk) Start
  Antisymmetric relation (talk) Start
  Automated theorem proving (talk) Start
  Axiom of constructibility (talk) Start
  Axiom of empty set (talk) Start
  Axiom of infinity (talk) Start
  Axiom of union (talk) Start
  Back-and-forth method (talk) Start
  Background and genesis of topos theory (talk) Start
  Bar induction (talk) Start
  Barber paradox (talk) Start
  Berry paradox (talk) Start
  Beth number (talk) Start
  Boolean prime ideal theorem (talk) Start
  Brouwer–Heyting–Kolmogorov interpretation (talk) Start
  Codomain (talk) Start
  Coequalizer (talk) Start
  Cofinite (talk) Start
  Comma category (talk) Start
  Complement (set theory) (talk) Start
  Curry's paradox (talk) Start
  De Bruijn index (talk) Start
  De Bruijn notation (talk) Start
  Dedekind-infinite set (talk) Start
  Definable real number (talk) Start
  Derangement (talk) Start
  Dialectica interpretation (talk) Start
  Elementary equivalence (talk) Start
  Fibonacci search technique (talk) Start
  Field of sets (talk) Start
  Fuzzy logic (talk) Start
  Fuzzy subalgebra (talk) Start
  Gödel numbering for sequences (talk) Start
  Gödel–Gentzen negative translation (talk) Start
  Harrop formula (talk) Start
  Herbrand's theorem (talk) Start
  History of the Church–Turing thesis (talk) Start
  Kan fibration (talk) Start
  Kleene star (talk) Start
  Kleene's T predicate (talk) Start
  Kripke–Platek set theory with urelements (talk) Start
  Mathematics as a language (talk) Start
  Minimal negation operator (talk) Start
  Model complete theory (talk) Start
  Monoidal t-norm logic (talk) Start
  Morass (set theory) (talk) Start
  Morley's categoricity theorem (talk) Start
  Non-standard arithmetic (talk) Start
  PA degree (talk) Start
  Paradoxical set (talk) Start
  Peirce's law (talk) Start
  Pointclass (talk) Start
  Predicate functor logic (talk) Start
  Presburger arithmetic (talk) Start
  Reduction (complexity) (talk) Start
  Reflection principle (talk) Start
  Reflexive relation (talk) Start
  Relational algebra (talk) Start
  Rosser's trick (talk) Start
  Schroeder-Bernstein theorem for measurable spaces (talk) Start
  Scott's trick (talk) Start
  Sequent (talk) Start
  Skolem normal form (talk) Start
  Sperner family (talk) Start
  Stable group (talk) Start
  Static discipline (talk) Start
  Super-recursive algorithm (talk) Start
  Tarski's high school algebra problem (talk) Start
  Tennenbaum's theorem (talk) Start
  Theory (mathematical logic) (talk) Start
  Two-element Boolean algebra (talk) Start
  Vacuous truth (talk) Start
  Wang tile (talk) Start
  Wason selection task (talk) Start
  Zero morphism (talk) Start
  Zuckerman functor (talk) Start
  Admissible ordinal (talk) Stub
  Algebraic normal form (talk) Stub
  Aronszajn line (talk) Stub
  Asymmetric relation (talk) Stub
  Atomic formula (talk) Stub
  Axiom of global choice (talk) Stub
  Axiom of projective determinacy (talk) Stub
  Axiom of real determinacy (talk) Stub
  Axiom of reducibility (talk) Stub
  BL (logic) (talk) Stub
  Barcan formula (talk) Stub
  Beck's monadicity theorem (talk) Stub
  Beth definability (talk) Stub
  Bicategory (talk) Stub
  Binary function (talk) Stub
  Boolean domain (talk) Stub
  Boolean expression (talk) Stub
  Boolean function (talk) Stub
  Cantor-Dedekind axiom (talk) Stub
  Categories for the Working Mathematician (talk) Stub
  Categorification (talk) Stub
  Category of small categories (talk) Stub
  Church–Rosser theorem (talk) Stub
  Classical modal logic (talk) Stub
  Club set (talk) Stub
  Coanalytic set (talk) Stub
  Cocountable (talk) Stub
  Code (set theory) (talk) Stub
  Coherent space (talk) Stub
  Complete theory (talk) Stub
  Conditional quantifier (talk) Stub
  Conjunctive normal form (talk) Stub
  Connected category (talk) Stub
  Consensus theorem (talk) Stub
  Continuous predicate (talk) Stub
  Covering lemma (talk) Stub
  Critical pair (talk) Stub
  Critical point (set theory) (talk) Stub
  Cylindric algebra (talk) Stub
  Dependence relation (talk) Stub
  Descriptive complexity theory (talk) Stub
  Diagonal functor (talk) Stub
  Difference hierarchy (talk) Stub
  Differentially closed field (talk) Stub
  Dimensional operator (talk) Stub
  Dinatural transformation (talk) Stub
  Direct proof (talk) Stub
  Disjunction and existence properties (talk) Stub
  Disjunction elimination (talk) Stub
  Disjunctive normal form (talk) Stub
  Distributive law between monads (talk) Stub
  Dual object (talk) Stub
  Effective dimension (talk) Stub
  End (category theory) (talk) Stub
  Euclidean relation (talk) Stub
  Explicit substitution (talk) Stub
  Extension (predicate logic) (talk) Stub
  Finite thickness (talk) Stub
  Fitch-style calculus (talk) Stub
  Fuzzy set operations (talk) Stub
  Generator (category theory) (talk) Stub
  Hausdorff maximal principle (talk) Stub
  Higher category theory (talk) Stub
  Impredicativity (talk) Stub
  Indecomposability (talk) Stub
  Inverse resolution (talk) Stub
  Judgment (mathematical logic) (talk) Stub
  Karoubi envelope (talk) Stub
  Knaster–Tarski theorem (talk) Stub
  Lightface analytic game (talk) Stub
  Literal (mathematical logic) (talk) Stub
  Locally catenative sequence (talk) Stub
  Maximal consistent set (talk) Stub
  Mouse (set theory) (talk) Stub
  Natural number object (talk) Stub
  Negation normal form (talk) Stub
  Non-Borel set (talk) Stub
  Non-logical symbol (talk) Stub
  Noncommutative logic (talk) Stub
  O-minimal theory (talk) Stub
  Ogden's lemma (talk) Stub
  Ordinal collapsing function (talk) Stub
  Ordinal definable set (talk) Stub
  Paraconsistent mathematics (talk) Stub
  Pumping lemma (talk) Stub
  Pumping lemma for regular languages (talk) Stub
  Rank-into-rank (talk) Stub
  Richardson's theorem (talk) Stub
  Rowbottom cardinal (talk) Stub
  Rules of passage (logic) (talk) Stub
  Sahlqvist formula (talk) Stub
  Strong generative capacity (talk) Stub
  Substitution instance (talk) Stub
  Tarski's exponential function problem (talk) Stub
  Tarski–Grothendieck set theory (talk) Stub
  Tolerant sequence (talk) Stub
  Transfinite number (talk) Stub
  Two-level grammar (talk) Stub
  Valuation (logic) (talk) Stub
  Weak generative capacity (talk) Stub
Last updated: Sun Jul 5 01:10:02 UTC 2009

Unassessed priority

Article Grade Comments
  Ε₀ (talk) Start
  Association for Logic, Language and Information (talk) UNone
Last updated: Sun Jul 5 01:10:02 UTC 2009
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