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Jul 24, 2013 at 14:28 comment added Keshav Srinivasan Thanks @JoelDavidHamkins! I suspected that Tarski's theorem would be involved. In fact, the whole reason I asked this question was trying to see what would happen if you restricted soundness to some arithmetically definable C-soundness property, but it looks like there's no evading the logic of Tarski.
Jul 24, 2013 at 14:19 vote accept Keshav Srinivasan
Jul 24, 2013 at 14:06 history edited Joel David Hamkins CC BY-SA 3.0
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Jul 24, 2013 at 13:59 history answered Joel David Hamkins CC BY-SA 3.0