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- Primitive_recursive_arithmetic abstract "Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ε0, which is the proof-theoretic ordinal of Peano arithmetic. PRA's proof theoretic ordinal is ωω, where ω is the smallest transfinite ordinal. PRA is sometimes called Skolem arithmetic.The language of PRA can express arithmetic propositions involving natural numbers and any primitive recursive function, including the operations of addition, multiplication, and exponentiation. PRA cannot explicitly quantify over the domain of natural numbers. PRA is often taken as the basic metamathematical formal system for proof theory, in particular for consistency proofs such as Gentzen's consistency proof of first-order arithmetic.".
- Primitive_recursive_arithmetic wikiPageExternalLink feferman92what.html.
- Primitive_recursive_arithmetic wikiPageID "6637022".
- Primitive_recursive_arithmetic wikiPageRevisionID "594964094".
- Primitive_recursive_arithmetic hasPhotoCollection Primitive_recursive_arithmetic.
- Primitive_recursive_arithmetic subject Category:Constructivism_(mathematics).
- Primitive_recursive_arithmetic subject Category:Formal_theories_of_arithmetic.
- Primitive_recursive_arithmetic type Abstraction100002137.
- Primitive_recursive_arithmetic type Cognition100023271.
- Primitive_recursive_arithmetic type Explanation105793000.
- Primitive_recursive_arithmetic type FormalTheoriesOfArithmetic.
- Primitive_recursive_arithmetic type HigherCognitiveProcess105770664.
- Primitive_recursive_arithmetic type Process105701363.
- Primitive_recursive_arithmetic type PsychologicalFeature100023100.
- Primitive_recursive_arithmetic type Theory105989479.
- Primitive_recursive_arithmetic type Thinking105770926.
- Primitive_recursive_arithmetic comment "Primitive recursive arithmetic, or PRA, is a quantifier-free formalization of the natural numbers. It was first proposed by Skolem as a formalization of his finitist conception of the foundations of arithmetic, and it is widely agreed that all reasoning of PRA is finitist. Many also believe that all of finitism is captured by PRA, but others believe finitism can be extended to forms of recursion beyond primitive recursion, up to ε0, which is the proof-theoretic ordinal of Peano arithmetic.".
- Primitive_recursive_arithmetic label "Primitive recursive arithmetic".
- Primitive_recursive_arithmetic sameAs m.0gfmgr.
- Primitive_recursive_arithmetic sameAs Q7243580.
- Primitive_recursive_arithmetic sameAs Q7243580.
- Primitive_recursive_arithmetic sameAs Primitive_recursive_arithmetic.
- Primitive_recursive_arithmetic wasDerivedFrom Primitive_recursive_arithmetic?oldid=594964094.
- Primitive_recursive_arithmetic isPrimaryTopicOf Primitive_recursive_arithmetic.