A Sacks real out of nowhere
نویسندگان
چکیده
There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.
منابع مشابه
00 7 a Sacks Real out of Nowhere
There is a proper countable support iteration of length ω adding no new reals at finite stages and adding a Sacks real in the limit.
متن کاملF U N D a M E N T a Mathematicae Strolling through Paradise
With each of the classical tree-like forcings adjoining a new real, one can associate a σ-ideal on the reals in a natural way. For example, the ideal s0 of Marczewski null sets corresponds to Sacks forcing S, while the ideal r0 of nowhere Ramsey sets corresponds to Mathias forcing R. We show (in ZFC) that none of these ideals is included in any of the others. We also discuss Mycielski’s ideal P...
متن کاملStrolling through Paradise
With each of the classical tree–like forcings adjoining a new real, one can associate a σ– ideal on the reals in a natural way. For example, the ideal of Marczewski null sets s corresponds to Sacks forcing S, while the ideal of nowhere Ramsey sets r corresponds to Mathias forcing R. We show (in ZFC) that none of these ideals is included in any of the others. We also discuss Mycielski’s ideal P2...
متن کاملSums of Darboux and continuous functions
It is shown that for every Darboux function F there is a non-constant continuous function f such that F + f is still Darboux. It is shown to be consistent—the model used is iterated Sacks forcing—that for every Darboux function F there is a nowhere constant continuous function f such that F + f is still Darboux. This answers questions raised in [5] where it is shown that in various models of se...
متن کاملINTERSECTION OF ESSENTIAL IDEALS IN THE RING OF REAL-VALUED CONTINUOUS FUNCTIONS ON A FRAME
A frame $L$ is called {it coz-dense} if $Sigma_{coz(alpha)}=emptyset$ implies $alpha=mathbf 0$. Let $mathcal RL$ be the ring of real-valued continuous functions on a coz-dense and completely regular frame $L$. We present a description of the socle of the ring $mathcal RL$ based on minimal ideals of $mathcal RL$ and zero sets in pointfree topology. We show that socle of $mathcal RL$ is an essent...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Log.
دوره 75 شماره
صفحات -
تاریخ انتشار 2010