TY - JOUR
T1 - Forcing absoluteness and regularity properties
AU - Ikegami, Daisuke
N1 - Funding Information:
This research was supported by a GLoRiClass fellowship funded by the European Commission (Early Stage Research Training Mono-Host Fellowship MEST-CT-2005-020841).
PY - 2010/4
Y1 - 2010/4
N2 - For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over L and the core model K. We use our results to answer open questions from set theory of the reals.
AB - For a large natural class of forcing notions, we prove general equivalence theorems between forcing absoluteness statements, regularity properties, and transcendence properties over L and the core model K. We use our results to answer open questions from set theory of the reals.
KW - Forcing absoluteness
KW - Regularity properties
UR - http://www.scopus.com/inward/record.url?scp=77649338859&partnerID=8YFLogxK
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U2 - 10.1016/j.apal.2009.10.005
DO - 10.1016/j.apal.2009.10.005
M3 - Article
AN - SCOPUS:77649338859
SN - 0168-0072
VL - 161
SP - 879
EP - 894
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 7
ER -