Articles liés à Second-order Arithmetic: Second-order Arithmetic, Mathematic...

Second-order Arithmetic: Second-order Arithmetic, Mathematical Logic, Axiom, Natural Number, Set Theory, Foundations of Mathematics, First-order Logic, Peano Axioms, Reverse Mathematics - Couverture souple

 
9786130319427: Second-order Arithmetic: Second-order Arithmetic, Mathematical Logic, Axiom, Natural Number, Set Theory, Foundations of Mathematics, First-order Logic, Peano Axioms, Reverse Mathematics

Synopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Second-order arithmetic includes, but is significantly stronger than, its first-order counterpart Peano arithmetic. Unlike Peano arithmetic, second-order arithmetic allows quantification over sets of numbers as well as numbers themselves. Because real numbers can be represented as (infinite) sets of natural numbers in well-known ways, and because second order arithmetic allows quantification over such sets, it is possible to formalize the real numbers in second-order arithmetic. For this reason, second-order arithmetic is sometimes called “analysisâ€.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.