Gödel's completeness theorem

URI: https://gptkb.org/entity/G%C3%B6del%27s_completeness_theorem
GPTKB entity
Statements (53)
Predicate Object
gptkbp:instance_of gptkb:theorem
gptkbp:applies_to first-order logic
gptkbp:developed_by gptkb:Kurt_Gödel
gptkbp:has_applications_in gptkb:computer_science
https://www.w3.org/2000/01/rdf-schema#label Gödel's completeness theorem
gptkbp:is_a theorem in mathematical logic
foundational result
result of Gödel's work
result in logic
result of formal logic
theorem concerning models
theorem in first-order logic
gptkbp:is_associated_with completeness of logical systems
gptkbp:is_cited_in philosophical discussions
numerous mathematical papers
textbooks on mathematical logic
gptkbp:is_compared_to gptkb:Gödel's_incompleteness_theorems
gptkbp:is_connected_to axiomatic systems
gptkbp:is_considered_as a cornerstone of mathematical logic
gptkbp:is_considered_by logicians
gptkbp:is_debated_in every consistent set of first-order sentences has a model
gptkbp:is_described_as textbooks on logic
gptkbp:is_discussed_in gptkb:academic_journals
logic conferences
logic seminars
gptkbp:is_essential_for proof theory
gptkbp:is_explored_in research papers
graduate studies
gptkbp:is_expressed_in gptkb:Logic
gptkbp:is_fundamental_to model theory
the study of formal systems
gptkbp:is_influential_in philosophy of mathematics
mathematical philosophy
gptkbp:is_part_of theoretical computer science
foundations of mathematics
the history of logic
the study of formal proofs
gptkbp:is_reflected_in the development of model theory
gptkbp:is_related_to axiomatic set theory
decidability
Hilbert's program
proofs of consistency
logical consequence
semantic entailment
gptkbp:is_taught_in university courses on logic
gptkbp:is_used_in mathematical logic
the study of computability
gptkbp:is_used_to analyze logical frameworks
validate logical systems
gptkbp:published_in gptkb:1930
gptkbp:was_a_demonstration_of Gödel's original proof
gptkbp:bfsParent gptkb:Kurt_Gödel
gptkbp:bfsLayer 5