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@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dcterms: <http://purl.org/dc/terms/> .
@prefix archive: <https://archive.561.group/ontology/> .
@prefix msc: <https://archive.561.group/taxonomies/msc/> .
<https://archive.561.group/taxonomies/msc>
a skos:ConceptScheme ;
skos:prefLabel "Mathematics Subject Classification"@en ;
skos:definition "Focused local SKOS slice of the Mathematics Subject Classification used for organizing mathematics below UDC 51. Expand from MSC as archive documents require finer classification."@en ;
dcterms:source <https://mathscinet.ams.org/msc/msc2020.html> ;
archive:refines <http://udcdata.info/025453> ;
skos:hasTopConcept
msc:00, msc:03, msc:05, msc:06, msc:08, msc:11, msc:12,
msc:13, msc:14, msc:15, msc:18, msc:20, msc:26, msc:54, msc:55,
msc:57, msc:37, msc:47, msc:60, msc:62, msc:68, msc:90, msc:97 .
msc:00
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "00" ;
skos:prefLabel "General and overarching mathematics"@en ;
archive:keywordId "mathematics", "mathematical-communication", "mathematical-practice" .
msc:03
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "03" ;
skos:prefLabel "Mathematical logic and foundations"@en ;
skos:narrower msc:03b05, msc:03b10, msc:03b15, msc:03b20, msc:03b25, msc:03b45, msc:03b47, msc:03b50, msc:03b53, msc:03g30 ;
archive:keywordId "mathematical-logic", "logic", "foundations", "type-theory", "set-theory" .
msc:03b05
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B05" ;
skos:prefLabel "Classical propositional logic"@en ;
archive:keywordId "propositional-logic", "classical-propositional-logic", "proposition" .
msc:03b10
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B10" ;
skos:prefLabel "Classical first-order logic"@en ;
archive:keywordId "first-order-logic", "classical-first-order-logic", "quantifier" .
msc:03b15
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B15" ;
skos:prefLabel "Higher-order logic and type theory"@en ;
archive:keywordId "higher-order-logic", "type-theory", "dependent-type-theory", "lambda-calculus" .
msc:03b20
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B20" ;
skos:prefLabel "Subsystems of classical logic"@en ;
skos:altLabel "Intuitionistic logic"@en ;
archive:keywordId "intuitionistic-logic", "constructive-logic" .
msc:03b25
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B25" ;
skos:prefLabel "Decidability of theories and sets of sentences"@en ;
archive:keywordId "decidability", "decidable-theories" .
msc:03b45
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B45" ;
skos:prefLabel "Modal logic"@en ;
archive:keywordId "modal-logic", "modal-calculus", "modal-semantics", "modal-system", "modal-operator", "necessity", "possibility", "possible-worlds", "kripke-semantics", "kripke-frame", "kripke-model", "accessibility-relation" .
msc:03b47
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B47" ;
skos:prefLabel "Substructural logics"@en ;
skos:altLabel "Linear logic"@en ;
archive:keywordId "substructural-logic", "linear-logic", "linear-logic-models", "chu-space", "chu-construction", "relevant-logic", "lambek-calculus" .
msc:03b50
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B50" ;
skos:prefLabel "Many-valued logic"@en ;
archive:keywordId "many-valued-logic", "many-valued", "four-valued-logic", "belnap-logic", "bilattice-theory", "bilattice", "four-bilattice", "twist-product", "truth-order", "knowledge-order" .
msc:03b53
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03B53" ;
skos:prefLabel "Paraconsistent logics"@en ;
archive:keywordId "paraconsistent-logic", "paraconsistency", "paraconsistent-linear-logic", "paraconsistent-linear-logic-models", "dialetheia", "explosion", "nelson-implication" .
msc:03g30
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:03 ;
skos:notation "03G30" ;
skos:prefLabel "Categorical logic"@en ;
archive:keywordId "categorical-logic", "hyperdoctrine", "predication-categories", "predication-category", "predicate-category", "predication-hyperdoctrine", "predication-fiber-algebra", "predication-fiber-functor" .
msc:05
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "05" ;
skos:prefLabel "Combinatorics"@en ;
archive:keywordId "combinatorics", "graph-theory" .
msc:06
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "06" ;
skos:prefLabel "Order, lattices, and ordered algebraic structures"@en ;
archive:keywordId "order-theory", "order", "lattices", "lattice-theory", "complete-lattice", "residuated-lattice", "galois-adjunction", "closure-algebra", "heyting-algebra", "heyting-implication", "formal-concept-analysis", "formal-context", "priestley-duality", "priestley-space" .
msc:08
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "08" ;
skos:prefLabel "General algebraic systems"@en ;
archive:keywordId "algebra", "universal-algebra", "algebraic-theory", "residuated-lattice" .
msc:11
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "11" ;
skos:prefLabel "Number theory"@en ;
archive:keywordId "number-theory", "arithmetic", "collatz-conjecture" .
msc:12
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "12" ;
skos:prefLabel "Field theory and polynomials"@en ;
archive:keywordId "field-theory", "fields", "polynomials" .
msc:13
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "13" ;
skos:prefLabel "Commutative algebra"@en ;
archive:keywordId "commutative-algebra", "rings", "ideals" .
msc:14
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "14" ;
skos:prefLabel "Algebraic geometry"@en ;
archive:keywordId "algebraic-geometry", "moduli", "moduli-theory", "settling-moduli", "deformation-theory", "moduli-stack", "orbifold-moduli" .
msc:15
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "15" ;
skos:prefLabel "Linear and multilinear algebra; matrix theory"@en ;
archive:keywordId "linear-algebra", "matrix-theory", "vector-spaces" .
msc:18
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "18" ;
skos:prefLabel "Category theory; homological algebra"@en ;
skos:narrower msc:18f20 ;
archive:keywordId "category-theory", "categories", "ordinary-categories", "enriched-categories", "infinity-categories", "topos-theory" .
msc:18f20
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:18 ;
skos:notation "18F20" ;
skos:prefLabel "Presheaves and sheaves, stacks, descent conditions"@en ;
archive:keywordId "sheaf-theory", "presheaves", "sheaves", "stacks", "descent", "settling-cohomology", "bigraded-settling-cohomology", "settling-associated-sheaf" .
msc:20
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "20" ;
skos:prefLabel "Group theory and generalizations"@en ;
archive:keywordId "group-theory", "groups", "group" .
msc:26
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "26" ;
skos:prefLabel "Real functions"@en ;
skos:altLabel "Real analysis"@en ;
archive:keywordId "mathematical-analysis", "real-analysis", "calculus", "functions" .
msc:37
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "37" ;
skos:prefLabel "Dynamical systems and ergodic theory"@en ;
archive:keywordId "dynamical-systems", "ergodic-theory", "recursive-dynamical-systems", "markov-operators", "settling-dynamics", "settling-regime-theory", "predication-settling", "substitution-dynamics", "aperiodic-dynamics", "step-n-substitution", "classifying-invariant", "mutually-locally-derivable" .
msc:47
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "47" ;
skos:prefLabel "Operator theory"@en ;
archive:keywordId "operator-theory", "spectral-theory", "markov-operators" .
msc:54
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "54" ;
skos:prefLabel "General topology"@en ;
archive:keywordId "topology", "topological-spaces", "locale-theory", "stone-duality", "alexandrov-topology", "frame-morphism", "bitopological-stone-duality" .
msc:55
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "55" ;
skos:prefLabel "Algebraic topology"@en ;
skos:narrower msc:55n30 ;
archive:keywordId "algebraic-topology", "homotopy-theory", "cohomology" .
msc:55n30
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:broader msc:55 ;
skos:notation "55N30" ;
skos:prefLabel "Sheaf cohomology"@en ;
archive:keywordId "sheaf-cohomology", "cohomology", "cech-cohomology", "hodge-theory" .
msc:57
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "57" ;
skos:prefLabel "Manifolds and cell complexes"@en ;
archive:keywordId "cell-complexes", "cw-complex", "manifolds" .
msc:60
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "60" ;
skos:prefLabel "Probability theory and stochastic processes"@en ;
archive:keywordId "probability", "probability-theory", "stochastic-processes" .
msc:62
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "62" ;
skos:prefLabel "Statistics"@en ;
archive:keywordId "statistics", "statistical-methods" .
msc:68
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "68" ;
skos:prefLabel "Computer science"@en ;
archive:keywordId "formal-math", "mathematical-software", "proof-assistants", "lean", "mathlib" .
msc:90
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "90" ;
skos:prefLabel "Operations research, mathematical programming"@en ;
archive:keywordId "optimization", "operations-research", "mathematical-programming" .
msc:97
a skos:Concept ;
skos:inScheme <https://archive.561.group/taxonomies/msc> ;
skos:topConceptOf <https://archive.561.group/taxonomies/msc> ;
skos:notation "97" ;
skos:prefLabel "Mathematics education"@en ;
archive:keywordId "mathematics-education", "learning-mathematics" .
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