Timeline for Possible cardinality and weight of an ordered field
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 1, 2014 at 19:36 | comment | added | Emil Jeřábek | (I now changed the claim in the linked post to something easily verifiable: if $\kappa^{<\kappa}=\kappa$, there exists an OF of size $2^\kappa$ with a dense subfield of size $\kappa$.) | |
| Dec 1, 2014 at 18:16 | comment | added | Emil Jeřábek | ... However, most Dedekind cuts on an OF cannot be realized in an ordered field extension where the original field is a dense subset. This only works for cuts satisfying the condition in mathoverflow.net/a/140962 . | |
| Dec 1, 2014 at 18:13 | comment | added | Emil Jeřábek | I got to this question because I realized that the claim I’m making in mathoverflow.net/a/188447 about $\kappa^+=2^\kappa$ is not obvious. Your claim that the supremum of cardinalities of ordered fields with a dense subset of size $\kappa$ is $\mathrm{ded}(\kappa)$ would solve the issue, but I do not understand how you came to it. There is no such statement in Keisler’s paper. His statement about the stability function of OF boils down to the rather trivial fact that $\mathrm{ded}(\kappa)$ is the sup of the numbers of Dedekind cuts on ordered fields of size $\kappa$. | |
| S Nov 9, 2014 at 23:22 | history | suggested | Avshalom | CC BY-SA 3.0 |
typos and formatting
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| Nov 9, 2014 at 23:04 | review | Suggested edits | |||
| S Nov 9, 2014 at 23:22 | |||||
| Nov 9, 2014 at 22:33 | history | edited | Asaf Karagila♦ | CC BY-SA 3.0 |
Corrected links.
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| Nov 9, 2014 at 20:48 | history | answered | Taras Banakh | CC BY-SA 3.0 |