Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Primitive_recursive_arithmetic> ?p ?o }
Showing triples 1 to 59 of
59
with 100 triples per page.
- 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 wikiPageLength "7139".
- Primitive_recursive_arithmetic wikiPageOutDegree "52".
- Primitive_recursive_arithmetic wikiPageRevisionID "668768489".
- Primitive_recursive_arithmetic wikiPageWikiLink Addition.
- Primitive_recursive_arithmetic wikiPageWikiLink Category:Constructivism_(mathematics).
- Primitive_recursive_arithmetic wikiPageWikiLink Category:Formal_theories_of_arithmetic.
- Primitive_recursive_arithmetic wikiPageWikiLink Consistency.
- Primitive_recursive_arithmetic wikiPageWikiLink Countable_set.
- Primitive_recursive_arithmetic wikiPageWikiLink Elementary_function_arithmetic.
- Primitive_recursive_arithmetic wikiPageWikiLink Epsilon_numbers_(mathematics).
- Primitive_recursive_arithmetic wikiPageWikiLink Equality_(mathematics).
- Primitive_recursive_arithmetic wikiPageWikiLink Equivalence_relation.
- Primitive_recursive_arithmetic wikiPageWikiLink Exponentiation.
- Primitive_recursive_arithmetic wikiPageWikiLink Finitism.
- Primitive_recursive_arithmetic wikiPageWikiLink First-order_logic.
- Primitive_recursive_arithmetic wikiPageWikiLink Formal_system.
- Primitive_recursive_arithmetic wikiPageWikiLink Foundations_of_mathematics.
- Primitive_recursive_arithmetic wikiPageWikiLink Gentzens_consistency_proof.
- Primitive_recursive_arithmetic wikiPageWikiLink Haskell_Curry.
- Primitive_recursive_arithmetic wikiPageWikiLink Heyting_arithmetic.
- Primitive_recursive_arithmetic wikiPageWikiLink Logical_conjunction.
- Primitive_recursive_arithmetic wikiPageWikiLink Logical_disjunction.
- Primitive_recursive_arithmetic wikiPageWikiLink Mathematical_induction.
- Primitive_recursive_arithmetic wikiPageWikiLink Metamathematics.
- Primitive_recursive_arithmetic wikiPageWikiLink Modus_ponens.
- Primitive_recursive_arithmetic wikiPageWikiLink Multiplication.
- Primitive_recursive_arithmetic wikiPageWikiLink Natural_number.
- Primitive_recursive_arithmetic wikiPageWikiLink Negation.
- Primitive_recursive_arithmetic wikiPageWikiLink Ordinal_analysis.
- Primitive_recursive_arithmetic wikiPageWikiLink Peano_axioms.
- Primitive_recursive_arithmetic wikiPageWikiLink Primitive_recursive_function.
- Primitive_recursive_arithmetic wikiPageWikiLink Proof_theory.
- Primitive_recursive_arithmetic wikiPageWikiLink Propositional_calculus.
- Primitive_recursive_arithmetic wikiPageWikiLink Quantifier_(logic).
- Primitive_recursive_arithmetic wikiPageWikiLink Reuben_Goodstein.
- Primitive_recursive_arithmetic wikiPageWikiLink Second-order_arithmetic.
- Primitive_recursive_arithmetic wikiPageWikiLink Solomon_Feferman.
- Primitive_recursive_arithmetic wikiPageWikiLink Tautology_(logic).
- Primitive_recursive_arithmetic wikiPageWikiLink Thoralf_Skolem.
- Primitive_recursive_arithmetic wikiPageWikiLinkText "PRA".
- Primitive_recursive_arithmetic wikiPageWikiLinkText "Primitive recursive arithmetic".
- Primitive_recursive_arithmetic wikiPageWikiLinkText "primitive recursive arithmetic".
- Primitive_recursive_arithmetic subject Category:Constructivism_(mathematics).
- Primitive_recursive_arithmetic subject Category:Formal_theories_of_arithmetic.
- Primitive_recursive_arithmetic hypernym Formalization.
- Primitive_recursive_arithmetic type Scientist.
- Primitive_recursive_arithmetic type Redirect.
- Primitive_recursive_arithmetic type Theory.
- 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 Q7243580.
- Primitive_recursive_arithmetic sameAs 原始帰納的算術.
- Primitive_recursive_arithmetic sameAs m.0gfmgr.
- Primitive_recursive_arithmetic sameAs Q7243580.
- Primitive_recursive_arithmetic wasDerivedFrom Primitive_recursive_arithmetic?oldid=668768489.
- Primitive_recursive_arithmetic isPrimaryTopicOf Primitive_recursive_arithmetic.