[FOM] Verification of choices for `V' and `L' for the Constructible Universe of sets

Brian Hart hart.bri at gmail.com
Wed Oct 15 13:43:24 EDT 2008

I deleted the thread on this topic so I can't reply to it, but just to
follow up with a bit more: "The use of \V " to refer to the universe
of all sets has its origin, via Whitehead and Russell's Principia
Mathematica, in Peano; Kreisel reports that what Godel had meant by
\L" was \lawlike."30 But as Kreisel goes on to say that \at the time
[i.e. of the consistency proof] he toyed with the idea that L
contained all legitimate denitions of sets," one may also suggest
that originally \L" rather stood for the German \legitim (deniert,
denierbar)," legitimate in the sense that the denitions are
predicative and in terms of rst-order logic. That \lawlike" starts
with the same letter would then be a fortunate coincidence of the
linguistic kind. (In German, `lawlike' is `gesetzmaig'.)" --
\Godel's Modernism: on Set-Theoretic
Incompleteness," revisited, Mark van Atten and Juliette Kennedy

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