Full Idea
Early study of first-order logic revealed a number of important features. Gödel showed that there is a complete, sound and effective deductive system. It follows that it is Compact, and there are also the downward and upward Löwenheim-Skolem Theorems.
Gist of Idea
First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems
Source
Stewart Shapiro (Higher-Order Logic [2001], 2.1)
Book Reference
'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.34