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Conservative extension

In mathematical logic, a conservative extension is a supertheory of a theory which is often convenient for proving theorems, but proves no new theorems about the language of the original theory. Similarly, a non-conservative extension, or proper extension,[citation needed] is a supertheory which is not conservative, and can prove more theorems than the…

Examples, Model-theoretic conservative extension & Overview

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Second-order arithmeticSubsystems of second-order arithmeticPeano arithmeticPRANBG
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Model-theoretic conservative extension

Model-theoretic
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Mathematical logicTheoryTheoremsProof theoreticFormulas
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Model-theoretic conservative extension

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Conservative extension

Nodes28
Edges27
Triples24
Avg. degree1.93
Density0.071429
Components1

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Conservative extension

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related to Examples · 17
Conservative extension → AC, ACA0, EFA, Extensions, Internal, IΣ1, NBG, Peano, PRA, RCA, RCA0, Shoenfield's, The, WKL, WKL0, ZF, ZFC
related to Model-theoretic conservative extension · 5
Conservative extension → Each, T1, T2, The, With
is a · 1
Conservative extension → supertheory of a theory which is often convenient for proving theorems
related to External links · 1
Conservative extension → The

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conservative extension theory extensions language t2 t1 every consistent also new theorem supertheory theorems model-theoretic zfc notion original citation needed

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SubjectPredicateObjectConfidenceSrc
Conservative extensionis asupertheory of a theory which is often convenient for proving theorems0.90text
Conservative extensionrelated to ExamplesACA00.60section
Conservative extensionrelated to ExamplesPeano0.60section
Conservative extensionrelated to ExamplesThe0.60section
Conservative extensionrelated to ExamplesRCA0.60section
Conservative extensionrelated to ExamplesWKL0.60section
Conservative extensionrelated to ExamplesEFA0.60section
Conservative extensionrelated to ExamplesWKL00.60section
Conservative extensionrelated to ExamplesRCA00.60section
Conservative extensionrelated to ExamplesPRA0.60section
Conservative extensionrelated to ExamplesNBG0.60section
Conservative extensionrelated to ExamplesZFC0.60section

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