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Consistency

In deductive logic, a consistent theory is one that does not lead to a logical contradiction. A theory T {\displaystyle T} is consistent if there is no formula φ {\displaystyle \varphi } such that both φ {\displaystyle \varphi } and its negation ¬ φ {\displaystyle \lnot \varphi } are elements of the set of consequences of T {\displaystyle T} . Let A…

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Consistency and completeness in arithmetic and set theory

First-order logic

Model theory

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Consistency

Nodes56
Edges55
Triples59
Avg. degree1.96
Density0.035714
Components1

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Consistency

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related to References · 44
Consistency → Alfred, BF01700692, Cambridge, Date, December, Deductive Sciences, Dover, Ebbinghaus, Elementary Lessons, Elements, Flum, From Frege, Gödel, Hans, Harvard University Press, Heijenoort, Introduction, ISBN, Jean, Jevons
see also · 10
Consistency → Being, Cognitive, Form, Idea, Mathematical, Mental, Paraconsistent, Philosophy, Polish, Type
related to Consistency and completeness in arithmetic and set theory · 4
Consistency → In, It, Peano, Presburger

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Important terminology

theory displaystyle consistent logic set phi varphi proof system one every mathematical arithmetic formula vdash formal lnot exists axioms satisfiable

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Zermeloinstance ofincluding set theories0.80text
Consistencyrelated to Consistency and completeness in arithmetic and set theoryIn0.60section
Consistencyrelated to Consistency and completeness in arithmetic and set theoryPeano0.60section
Consistencyrelated to Consistency and completeness in arithmetic and set theoryPresburger0.60section
Consistencyrelated to Consistency and completeness in arithmetic and set theoryIt0.60section
Consistencyrelated to ReferencesGödel0.60section
Consistencyrelated to ReferencesKurt0.60section
Consistencyrelated to ReferencesDecember0.60section
Consistencyrelated to ReferencesSätze0.60section
Consistencyrelated to ReferencesPrincipia Mathematica0.60section
Consistencyrelated to ReferencesSysteme0.60section
Consistencyrelated to ReferencesMonatshefte0.60section

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