First Incompleteness Theorem

URI: https://gptkb.org/entity/First_Incompleteness_Theorem
GPTKB entity
Statements (23)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo gptkb:Peano_arithmetic
gptkb:Zermelo-Fraenkel_set_theory
gptkbp:citation gptkb:On_Formally_Undecidable_Propositions_of_Principia_Mathematica_and_Related_Systems
gptkb:Principia_Mathematica
gptkbp:consequence gptkb:Gödel_numbering
limits of provability
non-computable functions
recursive enumerability
undecidable statements
gptkbp:countryOfPublication gptkb:German
gptkbp:field gptkb:logic
metamathematics
gptkbp:formedBy gptkb:Kurt_Gödel
1931
https://www.w3.org/2000/01/rdf-schema#label First Incompleteness Theorem
gptkbp:impact foundational crisis of mathematics
gptkbp:implies incompleteness of formal systems
gptkbp:publishedIn gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
gptkbp:relatedTo gptkb:Second_Incompleteness_Theorem
gptkbp:state Any consistent formal system that is sufficiently expressive to encode arithmetic contains true statements that cannot be proven within the system.
gptkbp:bfsParent gptkb:Gödel's_Incompleteness_Theorems
gptkbp:bfsLayer 7