First incompleteness theorem

URI: https://gptkb.org/entity/First_incompleteness_theorem
GPTKB entity
Statements (30)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo gptkb:Arithmetic
Formal axiomatic systems
gptkbp:consequence Existence of undecidable propositions
Incompleteness of Peano arithmetic
Incompleteness of Principia Mathematica
Incompleteness of Zermelo-Fraenkel set theory
Limits of provability in mathematics
gptkbp:countryOfPublication gptkb:German
gptkbp:field gptkb:logic
gptkbp:formedBy gptkb:Kurt_Gödel
1931
gptkbp:hasProofMethod gptkb:Arithmetization_of_syntax
Diagonalization
Self-reference
https://www.w3.org/2000/01/rdf-schema#label First incompleteness theorem
gptkbp:influenced gptkb:logic
Computer science
Metamathematics
gptkbp:partOf gptkb:Gödel's_incompleteness_theorems
gptkbp:publishedIn gptkb:Über_formal_unentscheidbare_Sätze_der_Principia_Mathematica_und_verwandter_Systeme_I
gptkbp:relatedTo gptkb:Second_incompleteness_theorem
gptkbp:seeAlso gptkb:Löb's_theorem
gptkb:Gödel_numbering
gptkb:Hilbert's_program
gptkb:Rosser's_trick
Turing's proof of the halting problem
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:Incompleteness_theorem
gptkbp:bfsLayer 6