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Single Idea 10588

[from 'Higher-Order Logic' by Stewart Shapiro, in 5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic ]

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