Nonexistence of Nonmolecular Generic Sets
Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 29
Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
Generic subsets of partially ordered sets play an important
role in giving significant examples of Zermelo-Fraenkel set-theoretical
models. The significance of these models lies in the fact that a
generic subset $G$ of a partially ordered set $P$, in general, does not
exist in a model $M$ in which $P$ exists. Thus, by adjoining $G$ to
$M$ an interesting extended model may ensue which has properties not
shared by $M$. Thus, in considering generic extensions of
set-theoretical models it is quite relevant to know whether or not a
generic subset of a partially ordered set $P$ exists in the same model
in which $P$ exists. In this paper, we give a necessary and sufficient
condition for $P$ to have a generic subset in the same model.
Classification :
06A10
@article{PIM_1984_N_S_36_50_a4,
author = {Donald D. Steiner and Alexander Abian},
title = {Nonexistence of {Nonmolecular} {Generic} {Sets}},
journal = {Publications de l'Institut Math\'ematique},
pages = {29 },
publisher = {mathdoc},
volume = {_N_S_36},
number = {50},
year = {1984},
language = {en},
url = {http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a4/}
}
Donald D. Steiner; Alexander Abian. Nonexistence of Nonmolecular Generic Sets. Publications de l'Institut Mathématique, _N_S_36 (1984) no. 50, p. 29 . http://geodesic.mathdoc.fr/item/PIM_1984_N_S_36_50_a4/