The Lindelöf number of a power; an introduction to the use of elementary submodels in general topology
Let \(\text{LIND} (\kappa)\) be the one-point compactification of the discrete space of size \(\kappa \geq \omega\). Theorem. The Lindelöf number of \(\text{(LIND} (\kappa))^\omega = \omega_1\). While this theorem is interesting in itself, the author is more interested in using its proof, as the subtitle indicates, as a way to introduce the reader to the use of elementary submodels in general topology. So first he gives a standard combinatorial proof, which is short, elegant, and nearly impenetrable --- where does its structure come from? Then he carefully motivates an elementary submodel proof, whose virtue is, as he points out, that ``the entity we search for is sitting in front of our noses'' - -- no deep intuitions about combinatorial structures are needed here. He then gives the elementary submodel proof in the standard way it would appear, and finally gives a heuristic for such proofs. Anyone unsure about this important technique, in any area in which set theory has been fruitfully applied, would be well advised to read this article.
scientific article; zbMATH DE number 609547
scientific article