The foundations of mathematics

URI: https://gptkb.org/entity/The_foundations_of_mathematics
GPTKB entity
Statements (91)
Predicate Object
gptkbp:instanceOf gptkb:mathematics
gptkbp:concerns completeness of mathematics
consistency of mathematics
soundness of mathematics
gptkbp:hasKeyword gptkb:Church–Turing_thesis
gptkb:Continuum_hypothesis
gptkb:Gödel's_incompleteness_theorems
gptkb:Hilbert's_program
gptkb:Platonism
gptkb:Russell's_paradox
gptkb:Tarski's_undefinability_theorem
gptkb:Zermelo–Fraenkel_set_theory
gptkb:Algorithmic_randomness
gptkb:Constructive_mathematics
gptkb:Constructive_set_theory
gptkb:Effective_descriptive_set_theory
gptkb:First_incompleteness_theorem
gptkb:Non-standard_analysis
gptkb:Ordinal_logic
gptkb:Predicative_mathematics
gptkb:Predicativism
gptkb:Proof_complexity
gptkb:Reverse_mathematics
gptkb:Second_incompleteness_theorem
gptkb:Ultrafinitism
gptkb:Univalent_foundations
gptkb:Peano_axioms
gptkb:Computability_theory
gptkb:Löwenheim–Skolem_theorem
gptkb:Compactness_theorem
gptkb:Completeness_theorem
gptkb:Axiomatic_set_theory
gptkb:Soundness_theorem
gptkb:Lambda_calculus
gptkb:Axiom_of_choice
gptkb:Homotopy_type_theory
gptkb:Cohen's_forcing
gptkb:Intuitionism
gptkb:Large_cardinal_axioms
gptkb:Logicism
gptkb:Formalism
Constructivism
fuzzy logic
Automated theorem proving
Metamathematics
Model theory
Proof theory
Category theory
Non-well-founded set theory
Transfinite induction
Intuitionistic logic
Modal logic
Non-classical logic
Paraconsistent logic
Recursion theory
Type theory
Descriptive set theory
Proof assistants
Categoricity
Computable analysis
Consistency proofs
Constructive analysis
Formalization of arithmetic
Independence proofs
Ordinal analysis
Proof mining
https://www.w3.org/2000/01/rdf-schema#label The foundations of mathematics
gptkbp:includes gptkb:logic
gptkb:set_theory
model theory
proof theory
recursion theory
gptkbp:keyFigure gptkb:Alan_Turing
gptkb:Alfred_North_Whitehead
gptkb:Alonzo_Church
gptkb:Bertrand_Russell
gptkb:David_Hilbert
gptkb:Ernst_Zermelo
gptkb:Georg_Cantor
gptkb:Kurt_Gödel
gptkb:Paul_Cohen
gptkb:Thoralf_Skolem
gptkb:L.E.J._Brouwer
gptkbp:relatedTo gptkb:logic
gptkb:philosophy
formal systems
axiomatic systems
gptkbp:studies basic concepts of mathematics
logical structure of mathematics
gptkbp:bfsParent gptkb:Max_Newman
gptkbp:bfsLayer 6