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It seems like Gödel didn't use the letter $L$ for his model before his book "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis with the Axioms of Set Theory", which is probably the first place it got used.

Do anyone of you know why he used the letter $L$? It does seem like a bit ad hoc in the book, where he names some functions $J_i$, then some other functions $K_i$ and then ends up defining $L$. But why $J_i$ then?

(I'm sorry if this is not suited for MO)

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    $\begingroup$ the sequence $J,K,L,\ldots$ seems quite natural to me, I would not attach any meaning to it $\endgroup$ – Carlo Beenakker Jul 22 '16 at 6:00
  • $\begingroup$ A lot of things are ad hoc, and they become standard. $\endgroup$ – Asaf Karagila Jul 22 '16 at 7:54
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I heard from Kai Hauser that the letter $L$ comes from "law", and it is because the model is constructed using some laws.

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    $\begingroup$ Only Gödel was Austrian and his work in german. The german word for law is "Gesetz" so that by your logic $L$ should have been named $G$. $\endgroup$ – Johannes Hahn Jul 22 '16 at 9:58
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    $\begingroup$ Let me mention at least that Kai Hauser also is German. $\endgroup$ – Joel David Hamkins Jul 22 '16 at 12:15
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    $\begingroup$ @JohannesHahn If Gödel's paper was in German, then I could accept your remark, but the fact is that his paper is in English. $\endgroup$ – Mohammad Golshani Jul 22 '16 at 13:06
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    $\begingroup$ @JohannesHahn It might be considered inappropriate for someone whose name begins with G to name his invention G. $\endgroup$ – Andreas Blass Jul 22 '16 at 15:47
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    $\begingroup$ If this were the explanation, one would expect the word “law” to appear somewhere in Godel’s writing on the subject — does it? $\endgroup$ – Matt F. May 5 '18 at 1:55

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