No random reals in countable support iterations |
| |
Authors: | Haim Judah Miroslav Repický |
| |
Affiliation: | (1) Department of Mathematics and Computer Science, Bar Ilan University, 52900 Ramat Gan, Israel;(2) Matematicky ústav SAV, Jesenná 5, 041 54 Košice, Slovakia |
| |
Abstract: | We prove a preservation theorem for limit steps of countable support iterations of proper forcing notions whose particular cases are preservations of the following properties on limit steps: “no random reals are added”, “μ(Random(V))≠1”, “no dominating reals are added”, “Cohen(V) is not comeager”. Consequently, countable support iterations of σ-centered forcing notions do not add random reals. The work was supported by BRF of Israel Academy of Sciences and by grant GA SAV 365 of Slovak Academy of Sciences. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|