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There’s a nice discussion now on constructivenews about the principle of omniscience. This is a weak form of excluded middle that obviously holds on finite sets is not considered constructive on $\mathbb{N}$. However, it actually holds on many infinite sets, as the discussion shows.
Hi Toby - had to fix your attribution of the MO question referenced at principle of omniscience - it was due to David Feldman, not me, although I commented on the question.
Interesting! Is there an “unlimited principle of omniscience”? Does that just refer to LPO for all sets, i.e. EM?
@ David: Oops! There are too many ‘David’s in the world, as you may have noticed.
@ Mike: I’ve never heard anybody use that phrase, but I would probably interpret it as you did if I met it. Still, I don’t really know for sure what inspired Bishop to use the word ‘limited’.
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