We introduce and study effective versions of the localization numbers introduced by Newelski and Roslanowski (Proceedings of the American Mathematical Society117(3) (1993), 823–831). We show that proper hierarchies are produced, and that the corresponding highness notions are relatively weak, in that they can often be made computably traceable. We discuss connections with other better-understood effective cardinal characteristics.
A.Blass, Combinatorial cardinal characteristics of the continuum, in: Handbook of Set Theory, Springer, 2010, pp. 395–489. doi:10.1007/978-1-4020-5764-9_7.
2.
J.Brendle, A.Brooke-Taylor, K.M.Ng and A.Nies, An analogy between cardinal characteristics and highness properties of oracles, in: Proceedings of the 13th Asian Logic Conference, World Scientific, 2015, pp. 1–28.
3.
S.Geschke and M.Kojman, Convexity numbers of closed sets in , Proceedings of the American Mathematical Society130 (2002).
4.
L.Newelski and A.Rosłanowski, The ideal determined by the unsymmetric game, Proceedings of the American Mathematical Society117(3) (1993), 823–831. doi:10.1090/S0002-9939-1993-1112500-6.
5.
A.Nies, Computability and Randomness, Oxford Logic Guides, Vol. 51, Oxford University Press, 2009.
6.
I.Ongay-Valverde, Splitting localization and prediction numbers, submitted.
7.
N.A.Rupprecht, Effective correspondents to cardinal characteristics in Cichon’s diagram, PhD thesis, The University of Michigan, 2010.
8.
S.A.Terwijn and D.Zambella, Computational randomness and lowness, The Journal of Symbolic Logic66(03) (2001), 1199–1205. doi:10.2307/2695101.
