Content deleted Content added
No edit summary |
No edit summary |
||
Line 5:
*A is '''<math>\alpha</math>-recursive''' if both A and <math>\alpha \setminus A</math> (its [[relative complement]] in <math>\alpha</math>) are <math>\alpha</math>-recursively-enumerable. It's of note that <math>\alpha</math>-recursive sets are members of <math>L_{\alpha+1}</math> by definition of <math>L</math>.
*Members of <math>L_\alpha</math> are called '''<math>\alpha</math>-finite''' and play a similar role to the finite numbers in classical recursion theory.
*Members of <Math>L_{\alpha+1}</math> are called '''<math>\alpha</math>-arithmetic'''. <ref>R. Gostanian, [https://www.sciencedirect.com/science/article/pii/0003484379900251 The Next Admissible Ordinal], Annals of Mathematical Logic 17 (1979). Accessed 1 January 2023.</ref>
There are also some similar definitions for functions mapping <math>\alpha</math> to <math>\alpha</math>:<ref name="relconstr">Srebrny, Marian, [http://matwbn.icm.edu.pl/ksiazki/fm/fm96/fm96114.pdf Relatively constructible transitive models] (1975, p.165). Accessed 21 October 2021.</ref>
| |||