Timeline for Cardinality: Why is there no "ℵ½"?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 24, 2010 at 6:44 | vote | accept | NevilleDNZ | ||
| May 19, 2010 at 12:22 | comment | added | KP Hart | Hartogs' original paper is here: resolver.sub.uni-goettingen.de/purl?GDZPPN002266105 | |
| May 18, 2010 at 17:24 | comment | added | Joel David Hamkins | It follows from Hartog's theorem (see link in Tom's answer), which for any set $A$ provides an ordinal $\kappa$ that does not embed into $A$. If cardinals are linearly ordered, then $A$ embeds into $\kappa$, and so $A$ is well-orderable. QED | |
| May 18, 2010 at 17:22 | comment | added | Harald Hanche-Olsen | I didn't know that the linear ordering of cardinals implies AC. Do you have a handy reference for that? | |
| May 18, 2010 at 16:04 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
added 167 characters in body
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| May 18, 2010 at 15:54 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |