First Incompleteness Theorem

GPTKB entity

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
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
https://www.w3.org/2000/01/rdf-schema#label	First Incompleteness Theorem