Gödel's Incompleteness Theorems

URI: https://gptkb.org/entity/Gödel's_Incompleteness_Theorems
GPTKB entity
Statements (27)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo arithmetic
formal axiomatic systems
gptkbp:citation many mathematical and philosophical works
gptkbp:consistsOf gptkb:First_Incompleteness_Theorem
gptkb:Second_Incompleteness_Theorem
gptkbp:field gptkb:logic
metamathematics
gptkbp:firstTheoremStates Any consistent formal system that is sufficiently expressive cannot be complete.
gptkbp:formedBy gptkb:Kurt_Gödel
https://www.w3.org/2000/01/rdf-schema#label Gödel's Incompleteness Theorems
gptkbp:impact foundations of mathematics
gptkbp:influenced gptkb:Alan_Turing
gptkb:logic
computability theory
gptkbp:language gptkb:German
gptkbp:publishedIn gptkb:Monatshefte_für_Mathematik
gptkbp:relatedTo gptkb:Hilbert's_program
gptkb:Peano_arithmetic
completeness
undecidability
consistency
gptkbp:secondTheoremStates No consistent system can prove its own consistency.
gptkbp:year 1931
gptkbp:bfsParent gptkb:Collected_Works_of_Kurt_Gödel
gptkb:Studies_in_Logic_and_the_Foundations_of_Mathematics
gptkbp:bfsLayer 6