Hilbert's completeness theorem
GPTKB entity
Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:theorem
|
| gptkbp:applies_to |
formal systems
countable languages |
| gptkbp:depicts |
the relationship between syntax and semantics
|
| gptkbp:discovered_by |
the context of non-classical logics
|
| gptkbp:ensures |
the existence of models for consistent theories
|
| gptkbp:historical_debate |
every consistent set of first-order sentences has a model
|
| gptkbp:historical_significance |
the development of logic
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hilbert's completeness theorem
|
| gptkbp:is_a_basis_for |
many logical systems
|
| gptkbp:is_a_framework_for |
mathematical structures
modern logic the nature of mathematical truth the study of logical paradoxes the study of formal languages |
| gptkbp:is_a_solution_for |
gptkb:computer_science
computability theory philosophical discussions on truth uncountable languages |
| gptkbp:is_associated_with |
satisfaction in models
|
| gptkbp:is_cited_in |
philosophy of mathematics
|
| gptkbp:is_discussed_in |
gptkb:Gödel's_incompleteness_theorems
gptkb:collection axiomatic systems |
| gptkbp:is_essential_for |
logical frameworks
understanding logical consequence |
| gptkbp:is_fundamental_to |
mathematical logic
|
| gptkbp:is_implemented_in |
artificial intelligence research
|
| gptkbp:is_influenced_by |
the study of formal proofs
|
| gptkbp:is_influential_in |
modern mathematical thought
formal semantics. the development of proof assistants |
| gptkbp:is_often_associated_with |
formal verification
|
| gptkbp:is_often_used_in |
the Löwenheim-Skolem theorem
logic textbooks university-level logic courses |
| gptkbp:is_referenced_in |
academic papers on logic
|
| gptkbp:is_related_to |
first-order logic
|
| gptkbp:is_subject_to |
extensive research
debate among philosophers of mathematics |
| gptkbp:key |
model theory
|
| gptkbp:named_after |
gptkb:David_Hilbert
|
| gptkbp:notable_quote |
the nature of mathematical objects
higher-order logics |
| gptkbp:occurs_in |
first-order logic
|
| gptkbp:proposed_by |
various branches of mathematics
|
| gptkbp:related_concept |
the philosophy of language
the compactness theorem |
| gptkbp:resulted_in |
1920s
proof theory |
| gptkbp:significance |
foundations of mathematics
|
| gptkbp:theory |
the limits of formal systems
|
| gptkbp:bfsParent |
gptkb:Gödel's_first_incompleteness_theorem
|
| gptkbp:bfsLayer |
5
|