Grigorieff showed that forcing to add a subset of ω using partial functions
with suitably chosen domains can add a generic real of minimal degree. We
show that forcing with partial functions to add a subset of an uncountable κ without
adding a real never adds a generic of minimal degree. This is in contrast to
forcing using branching conditions, as shown by Brown and Groszek.
Publié le : 2009-04-15
Classification:
forcing,
Grigorieff forcing,
degrees of constructiblity,
kappa degrees,
03E35,
03E45
@article{1242067710,
author = {Andersen, Brooke M. and Groszek, Marcia J.},
title = {Grigorieff Forcing on Uncountable Cardinals Does Not Add a Generic of Minimal Degree},
journal = {Notre Dame J. Formal Logic},
volume = {50},
number = {1},
year = {2009},
pages = { 195-200},
language = {en},
url = {http://dml.mathdoc.fr/item/1242067710}
}
Andersen, Brooke M.; Groszek, Marcia J. Grigorieff Forcing on Uncountable Cardinals Does Not Add a Generic of Minimal Degree. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp. 195-200. http://gdmltest.u-ga.fr/item/1242067710/