Timeline for Is there a $\Sigma^0_3$-complete ideal on $\omega$?

8 events

when toggle format	what		by	license	comment
S Jun 4, 2015 at 10:29	history	suggested	user74542		improved formatting
Jun 4, 2015 at 9:54	review	Suggested edits
S Jun 4, 2015 at 10:29
Jun 1, 2015 at 2:34	review	Close votes
Jun 1, 2015 at 13:45
Jun 1, 2015 at 1:50	comment	added	Jialiang He		And the other directed is easy, the map $f:2^\omega \longrightarrow \mathcal P({}^{<\omega}2)$ with $f(x)=\{\{x\|n\}:n\in\omega\}$, then $ A=f^{-1}(\mathcal I_A)$.
Jun 1, 2015 at 1:45	comment	added	Jialiang He		I can find a boud rank for $\mathcal I_A$ as follows: Define $X \subseteq \mathcal P({}^{<\omega}2)$ with $x\in X$ iff $\exists n \forall a\in [{}^{<\omega}2]^n((\forall s\in a\Rightarrow s\in x)\Rightarrow (\exists s\not= t\in a (s\prec t \vee t\prec s )))$. Define $g:X\longrightarrow [2^\omega]^{<\omega}$ with $g(x)=\{y\in 2^\omega:\forall n\exists m> n y\|m\in x\}$, then $\mathcal I_A=g^{-1}([A]^{<\omega})$, but I can't compute the rank of $\mathcal I_A$ is $\xi$.
May 31, 2015 at 23:02	comment	added	Ashutosh		I think you should try to show that the maps $(\{x_1, x_2, \dots, x_n\}, y_1, y_2, \dots, y_n) \mapsto z_1 \cup z_2 \cup \dots \cup z_n$ where $z_i = x_i \upharpoonright y_i$ are sufficiently injective on $[P]^n \times (2^{\omega})^n$ ($P$ is a perfect almost disjoint family) in order to preserve sufficiently high Borel ranks.
May 30, 2015 at 8:31	review	First posts
May 30, 2015 at 8:40
May 30, 2015 at 8:25	history	asked	Jialiang He	CC BY-SA 3.0