Timeline for Origin of the term "generic" in set theory
Current License: CC BY-SA 3.0
5 events
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| Jun 8, 2014 at 20:52 | comment | added | Timothy Chow | From Benjamin Dickman's response it seems clear that the later use of the word "generic" in set theory was influenced by Cohen's use of the word. "Generic" was certainly previously used in topology and geometry, as a quick MathSciNet search can confirm. I suppose it is conceivable that Cohen was unaware of that usage, or uninfluenced by it, but that would be very surprising. (Granted that he may not have realized exactly how close the parallel really was.) | |
| Jun 8, 2014 at 7:07 | comment | added | Asaf Karagila♦ | @Jason: Yes, it is possible. I have read the Wikipedia pages (that one you mention and for Generic point), but neither gave any hint as to how generic came into set theory. Did it come in all by itself? Was it an influence of topology? Or was algebraic geometers using the terms already and that influenced Cohen? Or maybe whoever developed the modern notion of a generic filter wasn't influenced by Cohen's choice, and rather used the notion of a topology? That's essentially the answer I was hoping to get. | |
| Jun 8, 2014 at 5:41 | comment | added | Jason Rute | @AsafKaragila, can't this be said about the use of the term "generic" in topology and geometry as well? The technical and English meanings are not very different, and it is obvious why the term was chosen (unlike, say, the terms "mice" and "creative" which are not so obvious). I think it is very possible (although I have no historical evidence for this), that the informal usage by Cohen slowly became formal and started out independent of topology, and happened to express the same idea. Also see here: en.wikipedia.org/wiki/Generic_property | |
| Jun 7, 2014 at 12:05 | comment | added | Asaf Karagila♦ | It seems that it might be the case, but the use of "generic" here can be understood the same way as a natural language use, rather than the specific mathematical use in topology and geometry. | |
| Jun 7, 2014 at 1:55 | history | answered | Timothy Chow | CC BY-SA 3.0 |