Timeline for Simple adjective for "of the size of a proper class"?
Current License: CC BY-SA 2.5
11 events
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| Mar 9, 2011 at 6:53 | history | edited | Todd Trimble | CC BY-SA 2.5 |
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| Mar 9, 2011 at 6:43 | comment | added | Todd Trimble | @Andreas: sure. The word "regular" also has more than one meaning. But generally people pick up which meaning is meant from context. @Peter: okay, that's true. But if the speaker hadn't mentioned such set-theoretic assumptions which would thus qualify the meaning of "large", the audience would no doubt interpret his "large collection" as referring to a proper class, and if that's not what the speaker meant, it would be his fault for not mentioning his assumptions. | |
| Mar 9, 2011 at 4:28 | comment | added | Peter LeFanu Lumsdaine | @Todd: I’ve often heard it used as Harry describes — eg someone will fix a Grothendieck universe, and use “small” to mean “of a size contained in that universe”, and “large” for other sets. Admittedly, four times out of five this is just because they were brought up with a third-hand presentation of ZFC and believe it’s unhygienic to ever mention something that’s not a set, when actually their “large” things could perfectly reasonably be proper classes after all… but nonetheless, it is often used to mean that, and sometimes advisedly so. | |
| Mar 9, 2011 at 3:55 | comment | added | Andreas Blass | Unfortunately, "large" also has another meaning, in the context "large cardinal." | |
| Mar 9, 2011 at 2:26 | comment | added | Mariano Suárez-Álvarez | @Hans, if you want to be understood among general mathematicians, define the term. | |
| Mar 9, 2011 at 2:25 | comment | added | Todd Trimble | Hans, when I said this is quite standard, I meant it. The usage is not restricted to category theorists: I am sure the usage is widely understood among general mathematicians who have reason to care about set-class distinctions (homotopy theorists, algebraic geometers, etc.). If you want to debate this, then show me evidence that the term is liable to be misunderstood by those who care about set-class distinctions. Why are you asking this question, anyway? | |
| Mar 9, 2011 at 2:04 | comment | added | Hans-Peter Stricker | @Todd: I do agree that this terminology is standard among category theorists. But I am looking for terms that are understood among general mathematicians. | |
| Mar 9, 2011 at 1:50 | comment | added | Todd Trimble | Guys: this terminology is quite standard. If someone emphasizes that a category is large, you can be quite sure that he means the class of morphisms is a proper class. This answers Hans's question. | |
| Mar 9, 2011 at 1:05 | comment | added | Hans-Peter Stricker | Sounds good, too, but it's too much "insider parlance": for the non-insider even "countably many" is "large". | |
| Mar 9, 2011 at 1:03 | comment | added | Harry Gindi | I tend to think of "large" as a relative term. For instance, if $\kappa$ is an uncountable regular cardinal, it makes sense to talk about things that are $\kappa$-small and $\kappa$-large with somewhat of a straight face. | |
| Mar 9, 2011 at 1:00 | history | answered | Todd Trimble | CC BY-SA 2.5 |