Timeline for What gets to be called a "proper class?"
Current License: CC BY-SA 4.0
10 events
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| Jun 27 at 13:46 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
improved exposition, fuller details
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| Jun 26 at 13:17 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jun 26 at 11:30 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jun 26 at 11:27 | vote | accept | Mike Battaglia | ||
| Jun 26 at 11:25 | comment | added | Joel David Hamkins | I think one can find all kinds of words used for them, subsets of the model, collections, and even "class", but that usage might be qualified. | |
| Jun 26 at 11:24 | comment | added | Mike Battaglia | And also curious if there is any name for the very strange subcollections I mentioned, or if I should just call them "collections..." | |
| Jun 26 at 11:23 | comment | added | Joel David Hamkins | Yes, usually the term is used with class extensionality. Coextensive classes are identical. | |
| Jun 26 at 11:22 | comment | added | Mike Battaglia | Thank you! That clears much of it up. One question: when we use the term "class" in the manner you write about above, is there some notion of extensionality? Or can logically equivalent formulas correspond to different classes, or something like that? For instance, in second order ZF, the class "P(x): x is strongly inaccessible" could be the empty set, or something else. Do we say that this class is equal to the "empty class" if no inaccessible cardinals exist, or is it a different class that is only extensionality equal? | |
| Jun 26 at 11:21 | history | edited | Joel David Hamkins | CC BY-SA 4.0 |
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| Jun 26 at 11:10 | history | answered | Joel David Hamkins | CC BY-SA 4.0 |