CONTENTS § 1. Introduction.................................................................................................... 5 § 2. Basic development............................................................................................... 8 § 3. Some elementarily equivalent spaces............................................................. 11 § 4. Elementary characterizations of some familiar spaces................................ 13 § 5. First order properties of C(X).............................................................................. 16 § 6. ℒ(X) and C(X) compared..................................................................................... 26 § 7. Some results on undecidability.......................................................................... 28 § 8. The class of topology lattices............................................................................. 32 § 9. Some bounds on the Löwenheim number for topology lattices.................. 33 §10. Open questions................................................................................................... 36 References.................................................................................................................... 39
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