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Dec 3, 2018 at 13:08 comment added Nik Weaver I think the idea is that WKL${}_0$ is supposed to be finitistically "reducible" because it is conservative over PRA for $\Pi^0_1$ sentences. In other words, we can trust it for the sentences we care about and just play a game with other sentences. Yes, I agree that RCA${}_0$ is broadly considered to be finitistically acceptable.
Dec 3, 2018 at 10:39 vote accept Joseph O'Rourke
Dec 3, 2018 at 9:12 comment added David Roberts Surely $RCA_0$ is the realm of finitism?
Dec 3, 2018 at 3:57 comment added Bjørn Kjos-Hanssen WKL asserts existence of infinite sets...
Dec 3, 2018 at 2:48 history edited Nik Weaver CC BY-SA 4.0
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Dec 3, 2018 at 2:46 comment added Andrés E. Caicedo By "predictive", did you mean "predicative"?
Dec 3, 2018 at 2:26 history answered Nik Weaver CC BY-SA 4.0