Timeline for Cardinality of an ultraproduct
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 16, 2015 at 16:09 | vote | accept | user38200 | ||
| Jan 16, 2015 at 12:55 | comment | added | Avshalom | In the OP, the cardinality of the ultraproduct is independent of the similarity type of the structures $A_{i}$, all of which have the same vocabulary. So it is enough to consider ultraproducts of cardinals. | |
| Jan 16, 2015 at 0:09 | answer | added | Monroe Eskew | timeline score: 11 | |
| Jan 15, 2015 at 22:34 | history | edited | user38200 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 22:22 | history | edited | user38200 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 22:17 | comment | added | Andrés E. Caicedo | Thank you. This is still not enough information, I'm afraid. For instance, I misspoke in my previous comment and assumed the ultrafilter was normal. Are you assuming this? | |
| Jan 15, 2015 at 22:12 | history | edited | user38200 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 22:06 | comment | added | Andrés E. Caicedo | You have not given us enough information. Is $\mathcal U$ an ultrafilter over $\kappa$? If so, and each $A_i$ has cardinality $\aleph_i$, the structure has cardinality $\kappa$. If all the $A_i$ are countable, so is the ultraproduct. Etc. | |
| Jan 15, 2015 at 21:46 | history | edited | user38200 | CC BY-SA 3.0 |
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| Jan 15, 2015 at 20:46 | history | asked | user38200 | CC BY-SA 3.0 |