Definition
In formal language theory, an alphabet, often called a vocabulary in the context of terminal and nonterminal symbols, is a non-empty set of indivisible symbols/characters/glyphs, typically thought of as representing letters, characters, digits, phonemes, or even words. The definition is used in a diverse range of fields including logic, mathematics, computer science, and linguistics. An alphabet may have any cardinality ("size") and, depending on its purpose, may be finite, countable, or even uncountable.
Related concepts
Abstract logicAckermann set theoryAleph numberAlgebraic logicAlgorithmArgumentArityAtomic formulaAtomic model (mathematical logic)Atomic sentenceAutomata theoryAutomated theorem provingAxiomAxiom of choiceAxiom schemaAxiomatic systemAxiomatization of Boolean algebrasBanach–Tarski paradoxBijectionBinary operationBinary stringBoolean algebraBoolean algebras canonically definedBoolean functionC (programming language)Cantor's diagonal argumentCantor's paradoxCantor's theoremCardinalityCartesian productCategorical theoryCategory (mathematics)Category of setsCategory theoryCharacter (computing)Character setChurch encodingChurch–Turing thesisClass (set theory)Classical logicCodomainCombinatorics on wordsCompactness theoremComplement (set theory)Complete theoryComputability theoryComputable functionComputable setComputably enumerable setComputational linguisticsConcatenationConcrete categoryConservative extensionConsistencyConstructible universeConstruction of the real numbersConstructive set theoryContinuum hypothesisCountableCountable setDecidability (logic)Decision problemDeductive systemDeterministic finite automatonDiagram (mathematical logic)Domain of a functionElement (mathematics)Elementary diagramElementary equivalenceElementary function arithmeticEmpty setEmpty stringEnumerationEquiconsistencyEquivalence relationEuclid's ElementsEuclidean geometryExistential quantificationExpression (mathematics)Extension by definitionsExtension by new constant and function namesExtensionalityFinitary relationFinite-valued logicFinite model theoryFinite setFirst-order logicFixed-point logicForcing (mathematics)Formal grammarFormal languageFormal language theoryFormal languagesFormal methodsFormal proofFormal semantics (logic)Formal systemFormal verificationFormation ruleFoundations of geometryFoundations of mathematicsFree logicFree variables and bound variablesFunction (mathematics)Functional predicateFuzzy setGeneral set theoryGlyphGrothendieck universeGround expressionGround formulaGödel's completeness theoremGödel's incompleteness theoremsGödel numberingHalting problemHeinz-Dieter EbbinghausHereditary setHigher-order logicHilbert's axiomsHilbert systemHistory of logicHistory of mathematical logicIdentifierImage (mathematics)Inaccessible cardinalIndependence (mathematical logic)InferenceInfinite-valued logicInfinite sequenceInfinite setInformation theoryInhabited setInjective functionInterpretation (logic)Interpretation (model theory)Interpretation functionIntersection (set theory)Introduction to Automata Theory, Languages, and ComputationIsomorphismKleene starKolmogorov complexityKripke's theory of truthKripke–Platek set theoryLambda calculusLarge cardinalLemma (mathematics)Lindström's theoremList of Hilbert systemsList of axiomsList of first-order theoriesList of formal systemsList of mathematical theoriesList of set identities and relationsList of statements independent of ZFCLogicLogical biconditionalLogical conjunctionLogical connectiveLogical consequenceLogical constantLogical disjunctionLogical equalityLogical equivalenceLogical truthLogicismLöwenheim–Skolem theoremMany-valued logicMap (mathematics)Material conditionalMathematical linguisticsMathematical logicMathematical notationMathematical objectMcGraw HillMetalanguageMinimal axioms for Boolean algebraModel complete theoryModel theoryMonadic predicate calculusMonadic second-order logicMorse–Kelley set theoryNP (complexity)Naive set theoryNatural deductionNatural language processingNegationNew FoundationsNew York CityNon-Euclidean geometryNon-logical symbolNon-standard modelNon-standard model of arithmeticOmega languageOpen formulaOperation (mathematics)Ordinal analysisOrdinal numberP (complexity)P versus NP problemParadoxes of set theoryPartition of a setPeano axiomsPhilosophy of mathematicsPhonemesPower setPredicate (mathematical logic)Predicate logicPredicate variablePrime modelPrimitive recursive arithmeticPrimitive recursive functionPrincipia MathematicaProduction (computer science)Programming language theoryProof of impossibilityProof theoryPropositionPropositional calculusPropositional formulaPropositional variableQuantifier (logic)Quantifier rankRecursionRecursive setRegular expressionRelation (mathematics)Reverse mathematicsRobinson arithmeticRule of inferenceRussell's paradoxSatisfiabilitySaturated modelSchröder–Bernstein theoremSecond-order arithmeticSecond-order logicSelf-verifying theoriesSemantic theory of truthSemantics (computer science)Semantics of logicSemiautomatonSentence (mathematical logic)SequenceSequent calculusSet (mathematics)Set theorySignature (logic)Singleton (mathematics)Skolem arithmeticSoundnessSpectrum of a sentenceSpectrum of a theorySpringer Science+Business MediaSquare of oppositionStrength (mathematical logic)String (computer science)String (formal languages)Structure (mathematical logic)Substitution (logic)Substructure (mathematics)SupertaskSurjective functionSyllogismSymbol (formal)Syntax (logic)Syntax analysisT-schemaTarski's axiomatization of the realsTarski's axiomsTarski's theory of truthTarski's undefinability theoremTarski–Grothendieck set theoryTautology (logic)Term (logic)Term logicTerminal and nonterminal symbolsTheoremTheories of truthTheory (mathematical logic)Three-valued logicTimeline of mathematical logicTransfer principleTransitive setTrue arithmeticTruth predicateTruth tableTruth valueTuring machineType (model theory)Type theoryUltrafilter (set theory)UltraproductUncountableUncountable setUndecidable problemUninterpreted functionUnion (set theory)Uniqueness quantificationUniversal quantificationUniversal setUniverse (mathematics)UrelementValidity (logic)Variable (mathematics)Venn diagramVon Neumann universeVon Neumann–Bernays–Gödel set theoryWell-formed formulaWolfgang RautenbergZermelo–Fraenkel set theory
137 concepts already in your glossary