Henselianity in the language of rings, with Franziska Jahnke

I would like to write about a new paper ([AJ15]) which Franziska Jahnke and I have written and put on the arXiv. It’s called Henselianity in the language of rings. In it we investigate the relationship between the following four properties of a field K:

(h) K is henselian, i.e. K admits a nontrivial henselian valuation,

(eh) K is elementarily henselian, i.e. every L\equiv K is henselian,

(def) K admits a definable nontrivial henselian valuation, and

(\emptyset-def) K admits a \emptyset-definable nontrivial henselian valuation.

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Two old-ish Terry Tao posts about model theory

I can’t get enough of Terry Tao’s blog What’s New, he writes so much and so brilliantly. Anyway, I found two really nice old-ish posts about model theory:

  • this which talks about completeness, compactness, zeroth-order logic, and Skolemisation;
  • and this which talks about nonstandard analysis, notions of `elementary convergence’ and `elementary completion’, countable saturation, compactness and saturation re-written from an analytical point-of-view, and the Szemerédi regularity lemma (something I always want to know more about).

I don’t have time to write anything more now, but later I will get back to it.