TY - JOUR
T1 - There may be simple Pא1 and Pא2-points and the Rudin-Keisler ordering may be downward directed
AU - Blass, Andreas
AU - Shelah, Saharon
PY - 1987
Y1 - 1987
N2 - We prove the consistency, relative to ZFC, of each of the following two (mutually contradictory) statements. (A) Every two non-principal ultrafilters on m have a common image via a finite-to-one function. (B) Simple Pא1-points and simple Pא2-points both exist. These results, proved by the second author, answer questions of the first author and P. Nyikos, who had obtained numerous consequences of (A) and (B), respectively. In the models we construct, the bounding number is א1, while the dominating number, the splitting number, and the cardinality of the continuum are א2.
AB - We prove the consistency, relative to ZFC, of each of the following two (mutually contradictory) statements. (A) Every two non-principal ultrafilters on m have a common image via a finite-to-one function. (B) Simple Pא1-points and simple Pא2-points both exist. These results, proved by the second author, answer questions of the first author and P. Nyikos, who had obtained numerous consequences of (A) and (B), respectively. In the models we construct, the bounding number is א1, while the dominating number, the splitting number, and the cardinality of the continuum are א2.
UR - https://www.scopus.com/pages/publications/0000339549
U2 - 10.1016/0168-0072(87)90082-0
DO - 10.1016/0168-0072(87)90082-0
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AN - SCOPUS:0000339549
SN - 0168-0072
VL - 33
SP - 213
EP - 243
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - C
ER -