Revision as of 17:22, 10 April 2018 edit CBM (talk \| contribs) Extended confirmed users, File movers, Pending changes reviewers, Rollbackers 55,390 edits →Computable real numbers: link Turing ← Previous edit		Revision as of 14:02, 2 September 2018 edit undo Robin S (talk \| contribs) Extended confirmed users 1,671 edits →Definability in arithmetic: correction: "[a real is] arithmetical [if and only if its Dedekind cut is at level <math>\Delta^0_1</math> of the arithmetical hierarchy]" -> "computable" Next edit →
Line 45: Every computable number is arithmetical, but not every arithmetical number is computable. For example, the limit of a Specker sequence is an arithmetical number that is not computable. The definitions of arithmetical and analytical reals can be stratified into the [[arithmetical hierarchy]] and [[analytical hierarchy]]. In general, a real is ~~arithmetical~~computable if and only if its Dedekind cut is at level <math>\Delta^0_1</math> of the arithmetical hierarchy, one of the lowest levels. Similarly, the reals with arithmetical Dedekind cuts form the lowest level of the analytical hierarchy. == Definability in models of ZFC ==

Definable real number: Difference between revisions