1. Better Explained
2. Better Explained
3. Mathematical logic
   1. Better Explained
      1. Propositional Equivalences
      2. Logical Equivalences
      3. material equivalence
   2. General
      1. Theorem
         1. Well-formed formula
            1. Symbol (formal)
      2. Formal system/Logical calculus
         1. Better Explained
            1. Formal proof
            2. Formal semantics (logic)
            3. An interpretation of a formal language is (roughly) an assignment of meanings to its symbols and truth-conditions to its sentences
            4. Syntax (logic)
         2. Formal language
            1. Formal grammar
            2. Formation rule
            3. Formal definition
            4. The syntax of grammars
            5. G = (N,?,P,S)
            6. The semantics of grammars
            7. Chomsky hierarchy
            8. Type-0 grammars
            9. Recursively enumerable languages
            10. Type-1 grammars
            11. Context-sensitive languages
            12. Type-2 grammars
            13. Context-free languages
            14. Backus–Naur Form
            15. Type-3 grammars
            16. Regular languages
            17. Finite state automaton
            18. Analytic grammars
            19. Alphabet
            20. Well-formed formula
            21. Atomic formula
            22. Closed formulas
         3. Deductive system/Deductive apparatus
            1. Rule of inference
            2. Better Explained
            3. Admissible rule
            4. Summary
            5. Simplification
            6. Addition
            7. Conjunction
            8. Resolution
            9. Disjunctive syllogism
            10. Hypothetical syllogism
            11. Modus tollens
            12. Modus ponens
            13. Rules for classical sentential calculus
            14. Rules for negations
            15. Reductio ad absurdum (or Negation Introduction)
            16. Reductio ad absurdum (related to the law of excluded middle)
            17. Noncontradiction (or Negation Elimination)
            18. Double negation elimination
            19. Double negation introduction
            20. Rules for conditionals
            21. Deduction theorem (or Conditional Introduction)
            22. Modus ponens (or Conditional Elimination)
            23. Modus tollens
            24. Rules for conjunctions
            25. Adjunction (or Conjunction Introduction)
            26. Simplification (or Conjunction Elimination)
            27. Rules for disjunctions
            28. Addition (or Disjunction Introduction)
            29. Separation of Cases (or Disjunction Elimination)
            30. Disjunctive syllogism
            31. Rules for biconditionals
            32. Biconditional introduction
            33. Biconditional Elimination
            34. Rules of classical predicate calculus
            35. Universal Introduction (or Universal Generalization)
            36. Universal Elimination (or Universal Instantiation)
            37. Existential Introduction (or Existential Generalization)
            38. Existential Elimination (or Existential Instantiation)
            39. Axioms
            40. Logical axioms
            41. Non-logical axioms
            42. Axiom schema
      3. Axiomatic system
      4. Type theory
      5. Syntax (logic)
      6. Symbol (formal)
      7. Theory (mathematical logic)/formal theory
      8. Proof calculus
         1. Natural deduction
      9. Entailment
   3. Traditional logic/Term logic
      1. Proposition
         1. Tautology (logic)
         2. Contradiction
      2. Inference
      3. Argument
         1. Validity
         2. Cogency
      4. Syllogism
      5. Square of opposition
      6. Venn diagram
   4. Propositional logic & Boolean logic
      1. Better Explained
         1. Logical equivalence
            1. Identity laws
            2. Domination laws
            3. Idempotent laws
            4. Double negation law
            5. Commutative laws
            6. Associative laws
            7. Distributive laws
            8. De Morgan's laws
            9. Absorption laws
            10. Negation laws
      2. Boolean function
      3. Propositional formula
      4. Logical connective
         1. Better Explained
            1. Order of precedence
         2. Negation (not) (¬ or ~)
         3. Conjunction (and) (, &, or · )
         4. Disjunction (or) (?)
         5. Exclusive disjunction/Exclusive or/XOR ?
         6. Material implication (if...then) (?,? or ?)/Material conditional/Condition statement/??????????????
         7. Logical biconditional/Material biconditional/Biconditional (if and only if) (iff) (xnor) (bi-implication)(?,=,?)
            1. ? is not a logical connective
            2. p = q is not a compound proposition
         8. Contingency (philosophy)
      5. Truth table
   5. Predicate logic
      1. Propositional function
         1. Predicate (mathematical logic)
      2. Quantification
         1. Existential quantification
         2. Universal quantification
      3. First-order logic
      4. Second-order logic
      5. Monadic predicate calculus
   6. Classical logic/standard logic
      1. First-order logic
      2. Syllogism
      3. Boolean logic
   7. Set theory
      1. Class (set theory)
         1. Set (mathematics)
            1. Finitary relation
            2. Entailment
            3. Finite set
            4. Infinite set
            5. Cardinality
            6. Uncountable set
            7. Countable set
            8. Recursive set
            9. Disjoint sets
            10. Membership
            11. Element (mathematics)
            12. Subset
            13. ? ? A.
            14. A ? A.
            15. A = B if and only if A ? B and B ? A
            16. Power set
            17. Basic operations
            18. Union (set theory)
            19. Intersection (set theory)
            20. Complement (set theory)
            21. Cartesian product
            22. n-ary product
            23. Special sets
            24. Describing sets
            25. Intensional definition/??? (???)
            26. {x|P(x)}
            27. Enumeration
            28. Venn diagram
         2. Better Explained
            1. Set Identities.
            2. Identity laws
            3. Domination laws
            4. Idempotent laws
            5. Complementation law
            6. Commutative laws
            7. Associative laws
            8. Distributive laws
            9. De Morgan's laws
            10. AnB=AUB
            11. Absorption laws
            12. Complement laws
      2. Extensionality
      3. Function (mathematics)
         1. Definition
            1. Notation
            2. Domain of a function
            3. Range (mathematics)
            4. Ordered pair
         2. Function composition
            1. Functional powers
            2. Transformation monoid
            3. Composition operator
         3. Inverse function
         4. Function spaces
         5. bijection, injection and surjection
         6. Floor and ceiling functions
         7. convex, monotonic, unimodal
            1. Convex function
            2. Monotonic function
         8. odd or even
         9. holomorphic, meromorphic, entire
         10. vector-valued
         11. computable
         12. differentiable, integrable
         13. linear, polynomial, rational
         14. algebraic, transcendental
         15. trigonometric
         16. fractal
         17. continuous
         18. Order theory
         19. Graph of a function
         20. Sequence
             1. Better Explained
             2. A function defined on an interval of the integers is usually called a sequence.
             3. Series (mathematics)
             4. Basic properties
             5. Potential confusion
             6. Convergent series
             7. Properties of series
             8. Non-negative terms
             9. Absolute convergence
             10. Conditional convergence
             11. Function series
             12. Power series
             13. Laurent series
             14. Dirichlet series
             15. Trigonometric series
             16. Fourier series
             17. Summation
             18. Sequences and automata
             19. Types of sequences
             20. ±1-sequence
             21. Arithmetic progression
             22. Cauchy sequence
             23. Farey sequence
             24. Fibonacci sequence
             25. Geometric progression
             26. Look-and-say sequence
             27. Thue–Morse sequence
      4. Axiomatic set theory
   8. Model theory
      1. Structure (mathematical logic)
      2. Interpretation (logic)
      3. Finite model theory
      4. Non-standard model
      5. Truth value
   9. Proof theory
      1. Formal proof
      2. Deductive system
      3. Formal system
      4. Theorem
      5. Entailment
      6. Rule of inference
         1. Modus ponens
         2. Modustollens
         3. Hypothetical syllogism
         4. Disjunctive syllogism
         5. Addition
         6. Simplification
         7. Conjunction
         8. Resolution
         9. Fallacy
      7. Syntax (logic)
      8. Mathematical proof
         1. Direct proof
         2. Mathematical induction
         3. Transposition (logic)
         4. Proof by contradiction
         5. Constructive proof
         6. Proof by exhaustion
         7. Combinatorial proof
         8. Probabilistic proof
         9. Nonconstructive proof
         10. Visual proof
         11. Elementary proof
         12. Two-column proof
         13. Better Explained
             1. Existence Proofs
             2. Uniqueness Proofs
   10. Computability theory
       1. Recursion
       2. Recursive set
       3. Recursively enumerable set
       4. Decision problem
       5. Church–Turing thesis
       6. Computable function
       7. Primitive recursive function
4. Philosophical logic
5. Metalogic and Metamathematics
6. Non-classical logic