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Apr 13, 2017 at 12:57 history edited CommunityBot
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Nov 15, 2012 at 19:38 comment added Not Mike Oh no, don't get me wrong that is exactly where my intuition about forcing comes from and is why I was a bit worried, since proofs always carry more weight than intuitions.
Nov 15, 2012 at 18:07 comment added Not Mike (and makes me finally feel like I can sanely use forcing to produce consistency results again.)
Nov 15, 2012 at 18:01 comment added Not Mike Joel, Thank you very much for the counter-example; this question has been bothering me for a couple of weeks, and for the life of me I couldn't figure out how to construct a forcing with these properties without first assuming either Con(ZFC) or \neg Con(ZFC); but as you seem to hint at, this is not at a problem because the extension of the forcing language to include the constant $\check{\lambda}$ for a fixed regular cardinal $\lambda$ is necessarily a more expressive language than that without constants. In particular forcing cheats way harder than I'd ever expected.
Nov 15, 2012 at 15:57 history edited Joel David Hamkins CC BY-SA 3.0
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Nov 15, 2012 at 15:49 history edited Joel David Hamkins CC BY-SA 3.0
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Nov 15, 2012 at 15:39 history answered Joel David Hamkins CC BY-SA 3.0