From ef3b65edbd091709448be39e766a2c643c45ab66 Mon Sep 17 00:00:00 2001 From: Josia Pietsch Date: Thu, 25 Jan 2024 20:25:21 +0100 Subject: [PATCH] some fix for some problem --- inputs/lecture_14.tex | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/inputs/lecture_14.tex b/inputs/lecture_14.tex index b040edf..258aaca 100644 --- a/inputs/lecture_14.tex +++ b/inputs/lecture_14.tex @@ -17,13 +17,13 @@ \] and similarly for $<^\ast$. % https://q.uiver.app/#q=WzAsNCxbMCwwLCJZIl0sWzIsMCwiWCJdLFswLDEsIkMnIl0sWzIsMSwiXFxiZWdpbnthcnJheX17Y31DXFxcXFxcUGlfMV4xLVxcdGV4dHtjb21wbGV0ZX1cXGVuZHthcnJheX0iXSxbMCwxLCJmIl0sWzIsMCwiXFxzdWJzZXRlcSIsMCx7InN0eWxlIjp7InRhaWwiOnsibmFtZSI6Imhvb2siLCJzaWRlIjoidG9wIn19fV0sWzMsMSwiXFxzdWJzZXRlcSIsMix7InN0eWxlIjp7InRhaWwiOnsibmFtZSI6Imhvb2siLCJzaWRlIjoidG9wIn19fV1d - \begin{tikzcd} - Y && X \\ - {C'} && {\begin{array}{c}C\\\Pi_1^1-\text{complete}\end{array}} - \arrow["f", from=1-1, to=1-3] - \arrow["\subseteq", hook, from=2-1, to=1-1] - \arrow["\subseteq"', hook, from=2-3, to=1-3] - \end{tikzcd} + % \begin{tikzcd} + % Y && X \\ + % {C'} && {\begin{array}{c}C\\\Pi_1^1-\text{complete}\end{array}} + % \arrow["f", from=1-1, to=1-3] + % \arrow["\subseteq", hook, from=2-1, to=1-1] + % \arrow["\subseteq"', hook, from=2-3, to=1-3] + % \end{tikzcd} Let $X = 2^{\Q} \supseteq \WO$. We have already show that $\WO$ is $\Pi^1_1$-complete.