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gptkbp:instance_of
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gptkb:theorem
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gptkbp:depicts
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the relationship between syntax and semantics
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https://www.w3.org/2000/01/rdf-schema#label
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Hilbert's completeness theorem
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gptkbp:is_a_foundation_for
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mathematical structures
modern logic
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gptkbp:is_a_result_that_ensures
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the existence of models for consistent theories
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gptkbp:is_a_theorem_in
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first-order logic
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gptkbp:is_a_theorem_that_applies_to
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countable languages
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gptkbp:is_a_theorem_that_can_be_applied_to
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uncountable languages
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gptkbp:is_a_theorem_that_has_applications_in
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gptkb:computer_science
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gptkbp:is_a_theorem_that_has_been_applied_in
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artificial intelligence research
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gptkbp:is_a_theorem_that_has_been_applied_to
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various branches of mathematics
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gptkbp:is_a_theorem_that_has_been_discussed_in_relation_to
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gptkb:Set
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gptkbp:is_a_theorem_that_has_been_explored_in
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the context of non-classical logics
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gptkbp:is_a_theorem_that_has_been_foundational_for
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the study of logical paradoxes
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gptkbp:is_a_theorem_that_has_been_generalized_to
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higher-order logics
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gptkbp:is_a_theorem_that_has_been_influential_in
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the development of proof assistants
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gptkbp:is_a_theorem_that_has_been_influential_in_shaping
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modern mathematical thought
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gptkbp:is_a_theorem_that_has_been_influential_in_the_development_of
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formal semantics.
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gptkbp:is_a_theorem_that_has_been_the_basis_for
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many logical systems
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gptkbp:is_a_theorem_that_has_been_the_subject_of
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extensive research
debate among philosophers of mathematics
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gptkbp:is_a_theorem_that_has_historical_significance_in
|
the development of logic
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gptkbp:is_a_theorem_that_has_implications_for
|
computability theory
philosophical discussions on truth
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gptkbp:is_a_theorem_that_has_implications_for_understanding
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the limits of formal systems
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gptkbp:is_a_theorem_that_has_influenced
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the study of formal proofs
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gptkbp:is_a_theorem_that_is_essential_for_understanding
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logical frameworks
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gptkbp:is_a_theorem_that_is_foundational_for
|
the study of formal languages
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gptkbp:is_a_theorem_that_is_foundational_for_understanding
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the nature of mathematical truth
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gptkbp:is_a_theorem_that_is_often_associated_with
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formal verification
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gptkbp:is_a_theorem_that_is_often_discussed_in_relation_to
|
the philosophy of language
|
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gptkbp:is_a_theorem_that_is_often_included_in
|
logic textbooks
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gptkbp:is_a_theorem_that_is_often_referenced_in
|
academic papers on logic
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gptkbp:is_a_theorem_that_is_often_referenced_in_discussions_about
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the nature of mathematical objects
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gptkbp:is_a_theorem_that_is_often_taught_in
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university-level logic courses
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gptkbp:is_a_theorem_that_is_often_used_in_conjunction_with
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the Löwenheim-Skolem theorem
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gptkbp:is_a_theorem_that_is_related_to
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the compactness theorem
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gptkbp:is_applicable_to
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formal systems
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gptkbp:is_associated_with
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satisfaction in models
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gptkbp:is_cited_in
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philosophy of mathematics
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gptkbp:is_debated_in
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every consistent set of first-order sentences has a model
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gptkbp:is_discussed_in
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axiomatic systems
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gptkbp:is_essential_for
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understanding logical consequence
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gptkbp:is_fundamental_to
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mathematical logic
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gptkbp:is_often_discussed_in
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gptkb:Gödel's_incompleteness_theorems
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gptkbp:is_related_to
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first-order logic
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gptkbp:is_significant_for
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foundations of mathematics
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gptkbp:key_concept
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model theory
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gptkbp:named_after
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gptkb:David_Hilbert
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gptkbp:was_a_result_of
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proof theory
|
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gptkbp:was_proven_in
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1920s
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gptkbp:bfsParent
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gptkb:Gödel's_first_incompleteness_theorem
|
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gptkbp:bfsLayer
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