Gödel's first incompleteness theorem

URI: https://gptkb.org/entity/Gödel's_first_incompleteness_theorem
GPTKB entity
Statements (27)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo gptkb:Peano_arithmetic
gptkb:Zermelo-Fraenkel_set_theory
gptkbp:category theorem in mathematics
theorem in logic
gptkbp:countryOfPublication gptkb:German
gptkbp:field gptkb:logic
metamathematics
gptkbp:formedBy gptkb:Kurt_Gödel
1931
gptkbp:hasConcept gptkb:Gödel_numbering
completeness
formal semantics
consistency
arithmetic
recursively enumerable
https://www.w3.org/2000/01/rdf-schema#label Gödel's first incompleteness theorem
gptkbp:implies There exist true statements in arithmetic that cannot be proven within the system.
gptkbp:influenced gptkb:logic
computer science
gptkbp:provenBy self-reference
arithmetization
gptkbp:publishedIn gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
gptkbp:relatedTo gptkb:Gödel's_second_incompleteness_theorem
gptkbp:state Any consistent, effectively generated formal system that is capable of expressing elementary arithmetic cannot be both complete and consistent.
gptkbp:bfsParent gptkb:Rosser's_theorem
gptkbp:bfsLayer 6