About: Theory (mathematical logic)

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In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms.

Attributes	Values
rdf:type	yago:WikicatConcepts yago:WikicatLogicalExpressions yago:Abstraction100002137 yago:Appearance104673965 yago:Attribute100024264 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Countenance104679549 yago:Explanation105793000 yago:Expression104679738 yago:HigherCognitiveProcess105770664 yago:Idea105833840 yago:Process105701363 yago:PsychologicalFeature100023100 yago:Quality104723816 yago:Theory105989479 yago:Thinking105770926 yago:WikicatFormalTheories
rdfs:label	Formální teorie (cs) Theorie (Logik) (de) Θεωρία (μαθηματική λογική) (el) Teoría (lógica) (es) Teoria (logika) (pl) Teoria (lógica matemática) (pt) Theory (mathematical logic) (en)
rdfs:comment	Formální teorie je jeden z nejdůležitějších pojmů matematickologické syntaxe. Mnoho matematických teorií může být formalizováno volbou vhodných axiomů. Některé teorie existují pouze jako teorie formální. Příkladem může být teorie množin, jejíž neformalizovaná podoba – tzv. naivní teorie množin je sporná. (cs) Στη μαθηματική λογική, μια θεωρία είναι σύνολο από σε μια τυπική γλώσσα. Για παράδειγμα, μια θεωρία πρώτης τάξης είναι σύνολο από προτάσεις πρώτης τάξης. Πολλοί συγγραφείς απαιτούν η θεωρία να είναι κλειστή ως προς τη λογική συνέπεια. (el) In der mathematischen Logik ist eine Theorie (der Prädikatenlogik erster Stufe) eine Menge von Aussagen über einer Signatur. (de) En lógica, una teoría es un conjunto de proposiciones dentro de un lenguaje formal que es semánticamente completo en el sentido de que todo modelo que satisface todas las proposiciones de la teoría también satisface cualquier otra proposición que sea consecuencia de la misma. Lo que diferencia a una teoría de un conjunto de proposiciones cualquiera es que incluye todas sus consecuencias, es decir, es un conjunto cerrado de proposiciones bajo el "operador consecuencia". (es) In mathematical logic, a theory (also called a formal theory) is a set of sentences in a formal language. In most scenarios, a deductive system is first understood from context, after which an element of a deductively closed theory is then called a theorem of the theory. In many deductive systems there is usually a subset that is called "the set of axioms" of the theory , in which case the deductive system is also called an "axiomatic system". By definition, every axiom is automatically a theorem. A first-order theory is a set of first-order sentences (theorems) recursively obtained by the inference rules of the system applied to the set of axioms. (en) Em lógica matemática, uma teoria (também chamada de teoria formal) é um conjunto de sentenças em uma linguagem formal. Normalmente um sistema dedutivo é entendido do contexto. Um elemento de uma teoria é chamado de axioma da teoria, e cada sentença que segue do axioma é chamado de teorema da teoria. Todo axioma também é um teorema. Uma teoria de primeira ordem é um conjunto de sentenças de primeira ordem. (pt) Teoria – niesprzeczny zbiór zdań. (pl)
dcterms:subject	Formal theories Logical expressions
Wikipage page ID	3512103 (xsd:integer)
Wikipage revision ID	1107683160 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press List of first-order theories Peano arithmetic Resolution (logic) Decidability (logic) Decidability of first-order theories of the real numbers Deduction theorem Interpretability Lindenbaum's lemma Consistent Mathematical logic Enumerable Theorem Formal theories Real closed fields Löwenheim–Skolem theorem Compactness theorem Complete theory Deductive system Structure (mathematical logic) Gödel's completeness theorem True arithmetic First-order logic Formal language Formal proof Formal system Logical consequence Natural deduction Expansion (model theory) Well-formed formula Recursion Logical expressions ZFC Axiom Axiomatic system Consequence relation Method of analytic tableaux Axioms Second-order logic Sequent calculus Mathematical theory Rule of inference Satisfiability Sentence (mathematical logic) Signature (logic) Principle of explosion Many-to-one Ω-consistent theory Enumeration theorem Inductive family Consistent set Model (model theory) Hilbert-style deductive system Ω-inconsistent theories dbr:Σ-sentence
sameAs	Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic) Theory (mathematical logic)

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