TY - JOUR
T1 - Large continuum, oracles
AU - Shelah, Saharon
PY - 2010/4
Y1 - 2010/4
N2 - Our main theorem is about iterated forcing for making the continuum larger than א2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing א1,א2 by λ, λ+ (starting with λ = λ<λ > א1). Well, we demand absolute c. c. c. So we get, e.g. the continuum is λ+ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a "partial" countable support iteration but it is c. c. c.
AB - Our main theorem is about iterated forcing for making the continuum larger than א2. We present a generalization of [2] which deal with oracles for random, (also for other cases and generalities), by replacing א1,א2 by λ, λ+ (starting with λ = λ<λ > א1). Well, we demand absolute c. c. c. So we get, e.g. the continuum is λ+ but we can get cov(meagre) = λ and we give some applications. As in non-Cohen oracles [2], it is a "partial" countable support iteration but it is c. c. c.
KW - Countable chain condition
KW - Iterated forcing
KW - Large continuum
KW - Peculiar cuts
UR - http://www.scopus.com/inward/record.url?scp=77953053011&partnerID=8YFLogxK
U2 - 10.2478/s11533-010-0018-3
DO - 10.2478/s11533-010-0018-3
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AN - SCOPUS:77953053011
SN - 1895-1074
VL - 8
SP - 213
EP - 234
JO - Central European Journal of Mathematics
JF - Central European Journal of Mathematics
IS - 2
ER -