User:Zarzuelazen/Books/Reality Theory: Mathematical Logic
 | The Wikimedia Foundation's book rendering service has been withdrawn. Please upload your Wikipedia book to one of the external rendering services. |
 | You can still create and edit a book design using the Book Creator and upload it to an external rendering service:
|
| This user book is a user-generated collection of Wikipedia articles that can be easily saved, rendered electronically, and ordered as a printed book. If you are the creator of this book and need help, see Help:Books (general tips) and WikiProject Wikipedia-Books (questions and assistance). Edit this book: Book Creator · Wikitext Order a printed copy from: PediaPress [ About ] [ Advanced ] [ FAQ ] [ Feedback ] [ Help ] [ WikiProject ] [ Recent Changes ] | ||||||||
Reality Theory: Mathematical Logic
- Abelian category
- Absorption (logic)
- Absorption law
- Abstract algebraic logic
- Actual infinity
- Additive category
- Adhesive category
- Adjoint functors
- Admissible ordinal
- Admissible rule
- Affirming the consequent
- Aleph number
- Algebra of sets
- Algebraic logic
- Allegory (category theory)
- Analytic proof
- Analytic set
- Analytical hierarchy
- Antecedent (logic)
- Antichain
- Antihomomorphism
- Antisymmetric relation
- Apartness relation
- Arithmetical hierarchy
- Arithmetical set
- Associative property
- Asymmetric relation
- Atom (order theory)
- Atomic formula
- Automorphism
- Autonomous category
- Axiom
- Axiom of choice
- Axiom of constructibility
- Axiom of countable choice
- Axiom of dependent choice
- Axiom of determinacy
- Axiom of extensionality
- Axiom of global choice
- Axiom of infinity
- Axiom of limitation of size
- 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
- Axiomatic system
- Berry paradox
- Beth number
- Bicategory
- Bijection
- Binary operation
- Binary relation
- Biproduct
- Boolean algebra
- Boolean function
- Boolean prime ideal theorem
- Boolean-valued model
- Borel equivalence relation
- Borel hierarchy
- Bounded complete poset
- Bounded quantifier
- Bourbaki–Witt theorem
- 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
- Categorical theory
- Categorification
- Category (mathematics)
- Category of abelian groups
- Category of modules
- Category of relations
- Category of sets
- Category of small categories
- Category theory
- Chain-complete partial order
- Choice function
- Class (set theory)
- Classical logic
- Closed category
- Closed monoidal category
- Closure (mathematics)
- Closure operator
- Club set
- Coanalytic set
- Codomain
- Coequalizer
- Cofinal (mathematics)
- Cofinality
- Coherence condition
- Coherent space
- Cointerpretability
- Cokernel
- Combinatory logic
- Comma category
- Commutative diagram
- Commutative property
- Commutativity of conjunction
- Compact closed category
- Compact element
- Compactness theorem
- Comparability
- Complement (set theory)
- Complete Boolean algebra
- Complete category
- Complete Heyting algebra
- 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)
- Converse implication
- Converse nonimplication
- Converse relation
- Coproduct
- Core model
- Corresponding conditional
- Countable chain condition
- Countable set
- Counterexample
- Covering relation
- Craig interpolation
- Critical point (set theory)
- Cumulative hierarchy
- Curry's paradox
- Curry–Howard correspondence
- Cut-elimination theorem
- Cylindric algebra
- Dagger compact category
- De Morgan's laws
- Decidability (logic)
- Dedekind-infinite set
- Deduction theorem
- Definitions of mathematics
- Dense order
- Denying the antecedent
- Derived category
- Derived functor
- Descriptive set theory
- Determinacy
- Diagonal functor
- Diagonal lemma
- Diagram (category theory)
- Dinatural transformation
- Direct limit
- Direct proof
- Directed set
- Disjoint sets
- Disjoint union
- Disjunctive normal form
- Distributive property
- Distributivity (order theory)
- 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 (category theory)
- Element (mathematics)
- Elementary class
- Elementary equivalence
- Elementary function arithmetic
- Embedding
- Empty domain
- Empty set
- End (category theory)
- Endomorphism
- Enriched category
- Enumeration
- Epimorphism
- Epsilon calculus
- Epsilon numbers (mathematics)
- Equaliser (mathematics)
- Equality (mathematics)
- Equational logic
- Equiconsistency
- Equinumerosity
- Equisatisfiability
- Equivalence class
- Equivalence of categories
- Equivalence relation
- Essentially surjective functor
- Euclidean relation
- Exclusive or
- Existential quantification
- Exponential object
- Exportation (logic)
- Extensionality
- Extranatural transformation
- F-algebra
- F-coalgebra
- False (logic)
- Family of sets
- Filter (mathematics)
- Filtered category
- Finitary
- Finitary relation
- Finite model theory
- Finite set
- Finite-valued logic
- Finitism
- Finitist set theory
- FinSet
- First-order logic
- Fitch notation
- Fixed-point lemma for normal functions
- Forcing (mathematics)
- Forgetful functor
- 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
- Function space
- Functional completeness
- Functional predicate
- Functor
- Functor category
- Galois connection
- General set theory
- Generator (category theory)
- Generic filter
- Gentzen's consistency proof
- Globular set
- Goodstein's theorem
- Greatest and least elements
- Grothendieck category
- Grothendieck universe
- Grothendieck's relative point of view
- Ground expression
- Groupoid
- Gödel numbering
- Gödel's completeness theorem
- Gödel's incompleteness theorems
- Hasse diagram
- Hausdorff maximal principle
- Herbrand interpretation
- Herbrand structure
- Herbrand's theorem
- Hereditarily finite set
- Hereditary property
- Hereditary set
- Heterogeneous relation
- Heyting algebra
- Hierarchy (mathematics)
- Higher category theory
- Higher-order logic
- Hilbert system
- Hilbert's paradox of the Grand Hotel
- Hom functor
- Homotopy category
- Hume's principle
- Hypersequent
- Ideal (order theory)
- Idempotence
- Idempotency of entailment
- Identity function
- If and only if
- Image (mathematics)
- Implicant
- Impredicativity
- Inaccessible cardinal
- Inclusion map
- Independence (mathematical logic)
- Index set
- Indexed family
- Indiscernibles
- Infimum and supremum
- Infinitary logic
- Infinite regress
- Infinite set
- Infinite-valued logic
- ∞-groupoid
- Initial algebra
- Initial and terminal objects
- Injective function
- Injective object
- Inner model
- Inner model theory
- Intermediate logic
- Interpretability
- Interpretation (logic)
- Interpretation (model theory)
- Intersection (set theory)
- Interval order
- Intransitivity
- Intuitionism
- Intuitionistic logic
- Inverse (logic)
- Inverse function
- Inverse limit
- Inverse system
- Involution (mathematics)
- Isomorphism
- Join and meet
- Kan extension
- Kan fibration
- Kernel (category theory)
- Kleene fixed-point theorem
- Kleisli category
- Knaster–Tarski theorem
- König's theorem (set theory)
- Kripke–Platek set theory
- L(R)
- Large cardinal
- Large countable ordinal
- Law of excluded middle
- Law of identity
- Law of noncontradiction
- Law of thought
- Lawvere theory
- Least fixed point
- Leibniz operator
- Liar paradox
- Lift (mathematics)
- Limit (category theory)
- Limit cardinal
- Limit ordinal
- Limit-preserving function (order theory)
- Lindenbaum–Tarski algebra
- Linear extension
- List of large cardinal properties
- List of mathematical proofs
- Literal (mathematical logic)
- Localization of a category
- Locally finite poset
- Logic
- Logical biconditional
- Logical conjunction
- Logical connective
- Logical consequence
- Logical constant
- Logical disjunction
- Logical equality
- Logical equivalence
- Logical form
- Logical NOR
- Logical truth
- Logicism
- Löb's theorem
- Löwenheim–Skolem theorem
- Many-sorted logic
- Map (mathematics)
- Martin's axiom
- Martin's maximum
- Material conditional
- Material implication (rule of inference)
- Material nonimplication
- Mathematical fallacy
- Mathematical induction
- Mathematical logic
- Mathematical object
- Mathematical proof
- Mathematical structure
- Mathematician
- Mathematics
- Maximal and minimal elements
- Measurable cardinal
- Metalogic
- Metamathematics
- Metatheorem
- Metavariable
- Method of analytic tableaux
- Minimal model (set theory)
- Model category
- Model complete 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
- Morse–Kelley set theory
- Multicategory
- Multiplicity (mathematics)
- Multiset
- Multivalued function
- Naive set theory
- Natural deduction
- Natural transformation
- Negation
- Nerve (category theory)
- Non-standard model of arithmetic
- Non-well-founded set theory
- Normal function
- Omega-categorical theory
- Open formula
- Operad
- Opposite category
- Order dimension
- Order embedding
- Order isomorphism
- Order theory
- Order type
- Ordered pair
- Ordinal analysis
- Ordinal arithmetic
- Ordinal notation
- Ordinal number
- Pairing function
- Paradoxes of set theory
- Partial equivalence relation
- Partial function
- Partially ordered set
- Partition of a set
- Peano axioms
- Peirce's law
- Philosophy of mathematics
- Plural quantification
- Pointclass
- Pointed set
- Posetal category
- Power set
- Preadditive category
- Predicate (mathematical logic)
- Predicate functor logic
- Predicate logic
- Predicate variable
- Prefix order
- Prenex normal form
- Preorder
- Preordered class
- Presburger arithmetic
- Presheaf (category theory)
- Primitive notion
- Primitive recursive arithmetic
- Principle of bivalence
- Principle of explosion
- Product (category theory)
- Product category
- Product order
- Product term
- Profunctor
- Projection (mathematics)
- Projection (set theory)
- Projective hierarchy
- Projective object
- Proof by contradiction
- Proof by contrapositive
- Proof by exhaustion
- Proof by infinite descent
- Proof calculus
- Proof of impossibility
- Proof sketch for Gödel's first incompleteness theorem
- Proof theory
- Proper forcing axiom
- Property of Baire
- Proposition
- Propositional calculus
- Propositional formula
- Propositional function
- Propositional proof system
- Propositional variable
- Pullback (category theory)
- Pushout (category theory)
- Quantifier (logic)
- Quantifier elimination
- Quasi-category
- Quotient category
- Rasiowa–Sikorski lemma
- Realizability
- Recursive definition
- Recursive ordinal
- Reductio ad absurdum
- Reflection principle
- Reflexive closure
- Reflexive relation
- Regular cardinal
- Regular category
- Relation algebra
- Representable functor
- Residuated Boolean algebra
- Residuated mapping
- Resolution (logic)
- Restriction (mathematics)
- Reverse mathematics
- Rigid category
- Ring of sets
- Robinson arithmetic
- Rosser's trick
- Ross–Littlewood paradox
- Rule of inference
- Rule of replacement
- Russell's paradox
- Satisfiability
- Schröder–Bernstein theorem
- Scope (logic)
- Second-order arithmetic
- Second-order logic
- Section (category theory)
- Semantics of logic
- Semigroupoid
- Semiorder
- Sentence (mathematical logic)
- Sequent
- Sequent calculus
- Serial relation
- Set (mathematics)
- Set function
- Set theory
- Set-builder notation
- Set-theoretic definition of natural numbers
- Setoid
- Sheffer stroke
- Signature (logic)
- Simplex category
- Singleton (mathematics)
- Skolem normal form
- Smooth maximum
- Solovay model
- Soundness
- Span (category theory)
- Spectrum of a sentence
- Spectrum of a theory
- Stable theory
- *-autonomous category
- Stationary set
- Stone duality
- Stone's representation theorem for Boolean algebras
- Strict 2-category
- String diagram
- Strong antichain
- Strong cardinal
- Strong monad
- Structural induction
- Structural proof theory
- Structuralism (philosophy of mathematics)
- Structure (mathematical logic)
- Subcategory
- Subclass (set theory)
- Subcountability
- Subobject
- Subobject classifier
- Subquotient
- Subset
- Substitution (logic)
- Substructure
- Substructure (mathematics)
- Successor cardinal
- Successor function
- Successor ordinal
- Supercompact cardinal
- Supertask
- Surjective function
- Syllogism
- Symbol (formal)
- Symmetric closure
- Symmetric difference
- Symmetric monoidal category
- Symmetric relation
- t-structure
- Tarski's undefinability theorem
- Tarski–Grothendieck set theory
- Tautology (logic)
- Tautology (rule of inference)
- Tensor-hom adjunction
- Term (logic)
- Term algebra
- Term logic
- Theorem
- Theory (mathematical logic)
- Thomson's lamp
- Tolerant sequence
- Topological category
- Topos
- Total order
- Transfinite induction
- Transfinite number
- Transitive closure
- Transitive relation
- Transitive set
- Transposition (logic)
- Tree (descriptive set theory)
- Tree (set theory)
- Triangulated category
- Truth function
- Truth table
- Truth value
- Type (model theory)
- Ultrafilter
- Ultrafinitism
- Ultraproduct
- Uncountable set
- Uninterpreted function
- Union (set theory)
- Univalent foundations
- Universal algebra
- Universal property
- Universal quantification
- Universal set
- Universe (mathematics)
- Unordered pair
- Upper and lower bounds
- Upper set
- Urelement
- Vacuous truth
- Validity (logic)
- Variety (universal algebra)
- Veblen function
- Venn diagram
- Von Neumann cardinal assignment
- Von Neumann universe
- Von Neumann–Bernays–Gödel set theory
- Weak interpretability
- Weak n-category
- Weak ordering
- Well-formed formula
- Well-founded relation
- Well-order
- Well-ordering theorem
- Well-quasi-ordering
- Witness (mathematics)
- Woodin cardinal
- Yoneda lemma
- Zeno's paradoxes
- Zermelo–Fraenkel set theory
- Zorn's lemma
- Ω-consistent theory
- Ω-logic