User:Zarzuelazen/Books/Reality Theory: Mathematical Logic

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Reality Theory: Mathematical Logic[edit]

Abelian category
Adjoint functors
Admissible ordinal
Admissible rule
Aleph number
Allegory (category theory)
Analytic set
Analytical hierarchy
Antecedent (logic)
Antihomomorphism
Antisymmetric relation
Arithmetical hierarchy
Arithmetical set
Associative property
Atomic formula
Automorphism
Autonomous category
Axiom
Axiom of choice
Axiom of constructibility
Axiom of determinacy
Axiom of extensionality
Axiom of infinity
Axiom of pairing
Axiom of power set
Axiom of projective determinacy
Axiom of regularity
Axiom of union
Axiom schema
Axiom schema of replacement
Axiom schema of specification
Berry paradox
Bicategory
Bijection
Binary operation
Binary relation
Boolean algebra
Borel equivalence relation
Borel hierarchy
Bounded quantifier
Braided monoidal category
Canonical form
Canonical normal form
Cantor's diagonal argument
Cantor's theorem
Cardinal assignment
Cardinal number
Cardinality
Cardinality of the continuum
Cartesian closed category
Cartesian product
Categorical logic
Categorification
Category (mathematics)
Category of abelian groups
Category of relations
Category of sets
Category of small categories
Category theory
Class (set theory)
Classical logic
Closed category
Closed monoidal category
Closure (mathematics)
Closure operator
Coanalytic set
Codomain
Coequalizer
Cokernel
Comma category
Commutative diagram
Commutative property
Commutativity of conjunction
Compact closed category
Compact element
Compactness theorem
Complement (set theory)
Complete partial order
Complete theory
Completeness (logic)
Completeness (order theory)
Composition of relations
Concrete category
Conditional proof
Cone (category theory)
Conglomerate (set theory)
Conjunctive normal form
Consequent
Consistency
Constructible universe
Constructive proof
Constructive set theory
Constructivism (philosophy of mathematics)
Continuum (set theory)
Continuum hypothesis
Contradiction
Contraposition
Converse (logic)
Coproduct
Core model
Countable set
Counterexample
Critical point (set theory)
Cumulative hierarchy
Curry–Howard correspondence
Cut-elimination theorem
Dagger compact category
De Morgan's laws
Decidability (logic)
Dedekind-infinite set
Deduction theorem
Definitions of mathematics
Derived functor
Descriptive set theory
Determinacy
Diagonal functor
Diagram (category theory)
Direct limit
Direct proof
Directed set
Disjoint sets
Disjoint union
Disjunctive normal form
Distributive property
Domain of a function
Domain of discourse
Double negation
Double-negation translation
Dual (category theory)
Dual object
Duality (mathematics)
Duality (order theory)
Effective descriptive set theory
Effective Polish space
Element (mathematics)
Elementary class
Elementary equivalence
Embedding
Empty domain
Empty set
Endomorphism
Enriched category
Enumeration
Epimorphism
Epsilon numbers (mathematics)
Equaliser (mathematics)
Equivalence class
Equivalence of categories
Equivalence relation
Essentially surjective functor
Exclusive or
Existential quantification
Exportation (logic)
Extensionality
F-algebra
F-coalgebra
Filter (mathematics)
Filtered category
Finitary
Finitary relation
Finite model theory
Finitism
Finitist set theory
First-order logic
Fixed-point lemma for normal functions
Forcing (mathematics)
Formal fallacy
Formal proof
Formal system
Formalism (philosophy of mathematics)
Foundations of mathematics
Free category
Free object
Free variables and bound variables
Frege's theorem
Full and faithful functors
Function (mathematics)
Function composition
Functional completeness
Functor
Functor category
Galois connection
Gentzen's consistency proof
Greatest and least elements
Grothendieck universe
Grothendieck's relative point of view
Ground expression
Groupoid
Gödel numbering
Gödel's completeness theorem
Gödel's incompleteness theorems
Hasse diagram
Herbrand interpretation
Herbrand structure
Herbrand's theorem
Hereditary set
Hierarchy (mathematics)
Higher category theory
Higher-order logic
Hilbert system
Hilbert's paradox of the Grand Hotel
Hom functor
Hume's principle
Ideal (order theory)
Idempotence
Idempotency of entailment
If and only if
Image (mathematics)
Impredicativity
Inaccessible cardinal
Independence (mathematical logic)
Indiscernibles
Infimum and supremum
Infinitary logic
Infinite regress
Infinite set
Initial and terminal objects
Injective function
Inner model
Interpretation (logic)
Interpretation (model theory)
Intersection (set theory)
Intuitionism
Inverse (logic)
Inverse function
Inverse limit
Inverse system
Involution (mathematics)
Isomorphism
Join and meet
Kan extension
Kernel (category theory)
Kleene fixed-point theorem
Kleisli category
Knaster–Tarski theorem
Kripke–Platek set theory
Kripke–Platek set theory with urelements
Large cardinal
Large countable ordinal
Law of excluded middle
Law of identity
Law of noncontradiction
Law of thought
Least fixed point
Liar paradox
Lift (mathematics)
Limit (category theory)
List of large cardinal properties
List of mathematical proofs
Literal (mathematical logic)
Logic
Logical biconditional
Logical conjunction
Logical connective
Logical consequence
Logical disjunction
Logical equality
Logical equivalence
Logical form
Logicism
Löb's theorem
Löwenheim–Skolem theorem
Map (mathematics)
Martin's axiom
Martin's maximum
Material conditional
Material implication (rule of inference)
Mathematical induction
Mathematical logic
Mathematical object
Mathematical proof
Mathematical structure
Mathematics
Maximal and minimal elements
Measurable cardinal
Metalanguage
Metamathematics
Metatheorem
Method of analytic tableaux
Minimal model (set theory)
Model theory
Modus ponens
Modus tollens
Monad (category theory)
Monadic predicate calculus
Monadic second-order logic
Monoid (category theory)
Monoidal category
Monoidal functor
Monomorphism
Monotonicity of entailment
Morley rank
Morley's categoricity theorem
Morphism
Multiset
Naive set theory
Natural deduction
Natural transformation
Necessity and sufficiency
Negation
Non-standard model of arithmetic
Non-well-founded set theory
Normal function
Object language
Opposite category
Order embedding
Order isomorphism
Order theory
Ordered pair
Ordinal notation
Ordinal number
Partial function
Partially ordered set
Partition of a set
Peano axioms
Peirce's law
Philosophy of mathematics
Plural quantification
Pointclass
Power set
Predicate (mathematical logic)
Predicate logic
Prefix order
Preorder
Presheaf (category theory)
Principle of bivalence
Principle of explosion
Product (category theory)
Product category
Profunctor
Projective hierarchy
Proof by contradiction
Proof by contrapositive
Proof by exhaustion
Proof calculus
Proof sketch for Gödel's first incompleteness theorem
Proof theory
Proper forcing axiom
Proposition
Propositional calculus
Propositional formula
Propositional variable
Pullback (category theory)
Pushout (category theory)
Quantifier (logic)
Quotient category
Realizability
Recursive definition
Recursive ordinal
Reductio ad absurdum
Reflexive relation
Regular category
Representable functor
Resolution (logic)
Reverse mathematics
Rigid category
Robinson arithmetic
Rule of inference
Rule of replacement
Russell's paradox
Satisfiability
Second-order arithmetic
Second-order logic
Semantics of logic
Semigroupoid
Sentence (mathematical logic)
Sequent
Sequent calculus
Set (mathematics)
Set theory
Set-builder notation
Set-theoretic definition of natural numbers
Signature (logic)
Soundness
Span (category theory)
Stable theory
Stationary set
Strict 2-category
Strong monad
Structural induction
Structuralism (philosophy of mathematics)
Structure (mathematical logic)
Subcategory
Subobject
Subobject classifier
Subset
Substitution (logic)
Substructure
Successor cardinal
Successor function
Successor ordinal
Surjective function
Syllogism
Symbol (formal)
Symmetric monoidal category
Symmetric relation
Tarski's undefinability theorem
Tarski–Grothendieck set theory
Tautology (logic)
Tautology (rule of inference)
Tensor-hom adjunction
Term (logic)
Term logic
Theorem
Theory (mathematical logic)
Topos
Total order
Transfinite induction
Transfinite number
Transitive relation
Transitive set
Transposition (logic)
Tree (descriptive set theory)
Tree (set theory)
Truth table
Truth value
Type (model theory)
Ultrafilter
Ultrafinitism
Ultraproduct
Uncountable set
Uninterpreted function
Union (set theory)
Universal algebra
Universal property
Universal quantification
Universal set
Universe (mathematics)
Unordered pair
Urelement
Validity
Variety (universal algebra)
Venn diagram
Von Neumann universe
Weak ordering
Well-formed formula
Well-founded relation
Well-order
Well-ordering theorem
Well-quasi-ordering
Woodin cardinal
Yoneda lemma
Zermelo–Fraenkel set theory
Zorn's lemma
Ω-consistent theory
Ω-logic