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 sav08:tarski_s_fixpoint_theorem [2008/05/07 22:50]giuliano sav08:tarski_s_fixpoint_theorem [2009/03/26 10:36] (current)vkuncak Both sides previous revision Previous revision 2009/03/26 10:36 vkuncak 2008/05/07 22:50 giuliano 2008/05/07 22:48 giuliano 2008/05/06 23:44 giuliano 2008/04/30 10:49 vkuncak 2008/04/30 09:51 vkuncak 2008/04/30 09:50 vkuncak 2008/04/30 09:49 vkuncak 2008/04/30 09:48 vkuncak 2008/04/30 09:48 vkuncak 2008/04/30 09:41 vkuncak 2008/04/30 09:25 vkuncak 2008/04/30 09:23 vkuncak 2008/04/30 09:22 vkuncak created 2009/03/26 10:36 vkuncak 2008/05/07 22:50 giuliano 2008/05/07 22:48 giuliano 2008/05/06 23:44 giuliano 2008/04/30 10:49 vkuncak 2008/04/30 09:51 vkuncak 2008/04/30 09:50 vkuncak 2008/04/30 09:49 vkuncak 2008/04/30 09:48 vkuncak 2008/04/30 09:48 vkuncak 2008/04/30 09:41 vkuncak 2008/04/30 09:25 vkuncak 2008/04/30 09:23 vkuncak 2008/04/30 09:22 vkuncak created Line 40: Line 40: **Lemma:** The value $a_*$ is a prefix point. **Lemma:** The value $a_*$ is a prefix point. - Observation:​ $a_*$ need not be a fixpoint. + Observation:​ $a_*$ need not be a fixpoint ​(example in exercises, e.g. on lattice [0,1] of real numbers). **Definition:​** A function $G$ is $\omega$-continuous if for every chain $x_0 \sqsubseteq x_1 \sqsubseteq \ldots \sqsubseteq x_n \sqsubseteq \ldots$ we have **Definition:​** A function $G$ is $\omega$-continuous if for every chain $x_0 \sqsubseteq x_1 \sqsubseteq \ldots \sqsubseteq x_n \sqsubseteq \ldots$ we have