Timeline for Mathematical objects whose name is a single letter
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2018 at 6:45 | comment | added | Andrés E. Caicedo | And $K$ is for kernel. It was introduced (or, at least, one of its versions was) in MR0611394 (82i:03063). Dodd, A.; Jensen, R. The core model. Ann. Math. Logic 20 (1981), no. 1, 43–75. | |
| Jan 4, 2018 at 6:41 | comment | added | Andrés E. Caicedo | In his 1939 "Consistency proof for the generalized continuum hypothesis", Gödel uses $M$ to denote the constructible universe. He switches to $L$ in his 1940 monograph, "The consistency of the axiom of choice and of the generalized continuum hypothesis with the axioms of set theory". No reason is given for the choice of symbol in either case. | |
| Jan 4, 2018 at 6:33 | comment | added | Andrés E. Caicedo | To $V$ and $L$ one should add $K$, the core model. | |
| Jan 4, 2018 at 6:32 | comment | added | Andrés E. Caicedo | $V$ (or V) was introduced by Peano in his "Arithmetices principia. Nova methodo exposita" from 1889. He uses V for verum and $\Lambda$ for falsum, and the symbols were adopted to denote the universe of all sets, and the empty set, accordingly (Peano also uses V explicitly for "the class of all individuals"). See pp. viii and xi here. | |
| Jan 3, 2018 at 23:13 | comment | added | Joel David Hamkins | I also used to think that $V$ stood for von Neumann, but when I looked into it a few years, I recall finding that the usage pre-dated him. Unfortunately, I don't recall now whether I had found it in Frege or Zermelo or where. I vaguely recall it having come up here on MO previously. | |
| Jan 3, 2018 at 22:22 | comment | added | Adam P. Goucher | @ToddTrimble I thought that the $V$ was from 'von Neumann'. | |
| Jan 3, 2018 at 21:29 | comment | added | Todd Trimble | What are the stories behind these choices? I've always thought that V was chosen to suggestively depict the cumulative hierarchy, with an empty set at the bottom and spreading out by taking a power set of what one had previously at a successor ordinal (and collecting all previous stages at limit ordinals). But I can't guess where L comes from. | |
| S Jan 3, 2018 at 20:41 | history | answered | Joel David Hamkins | CC BY-SA 3.0 | |
| S Jan 3, 2018 at 20:41 | history | made wiki | Post Made Community Wiki by Joel David Hamkins |