Timeline for Does a "composite field" always exist?
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| Feb 7, 2012 at 11:53 | comment | added | Ramiro de la Vega | @Martin: To be honest, I´ve never seen a published proof of the fact that fields have the amalgamation property. Model Theory textbooks (e.g. Hodges, Chang & Keisler) just mention the fact and use it to prove other things, like quantifier elimination for algebraically closed fields. | |
| Feb 7, 2012 at 11:07 | comment | added | Martin Brandenburg | +1 since you provide the general background, but it would be even a better answer if you add a specific reference where the amalgamation property for fields is proved. I believe that model theorists argue as in David's answer or equivalently with "$\kappa$-categorical" arguments. | |
| Feb 6, 2012 at 22:47 | history | answered | Ramiro de la Vega | CC BY-SA 3.0 |