Timeline for Can we recognize when a category is equivalent to the category of models of a first order theory?
Current License: CC BY-SA 2.5
9 events
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| Jan 29, 2010 at 15:03 | comment | added | François G. Dorais | I guess the key about VP is that if k is sufficiently large then k-directed colimits in Mod(T) can be computed in Mod(0). For the reverse direction, it is the graph theoretic interpretation of VP which is key. | |
| Jan 29, 2010 at 3:43 | comment | added | François G. Dorais | I deleted that confusing short paragraph and, in exchange, I added a considerable amount of details, including the relationship with VP. | |
| Jan 29, 2010 at 3:23 | history | edited | François G. Dorais | CC BY-SA 2.5 |
added lots of details
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| Jan 28, 2010 at 13:18 | comment | added | Joel David Hamkins | Thanks very much for this answer! But am I to understand you correctly that, ultimately, accessibility is neither necessary nor sufficient as a criterion to answer my specific question? After all, if it works for infinitary languages also, then it would seem to admit instances that are not Mod(T) for any first order theory. And your final remark says that Mod(T) is not always accessible? Could you explain your final remark about VP a bit more? If large cardinals come in here, that would be great. | |
| Jan 27, 2010 at 23:12 | history | edited | François G. Dorais | CC BY-SA 2.5 |
grammar
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| Jan 27, 2010 at 23:06 | history | edited | François G. Dorais | CC BY-SA 2.5 |
correction
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| Jan 27, 2010 at 22:52 | history | edited | François G. Dorais | CC BY-SA 2.5 |
addendum
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| Jan 27, 2010 at 19:23 | history | edited | François G. Dorais | CC BY-SA 2.5 |
grammar and precisions
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| Jan 27, 2010 at 19:10 | history | answered | François G. Dorais | CC BY-SA 2.5 |