more from Stephen Read

### Single Idea 10977

#### [catalogued under 5. Theory of Logic / K. Features of Logics / 6. Compactness]

Full Idea

Compact consequence undergenerates - there are intuitively valid consequences which it marks as invalid, such as the ω-rule, that if A holds of the natural numbers, then 'for every n, A(n)', but the proof of that would be infinite, for each number.

Gist of Idea

Compactness blocks the proof of 'for every n, A(n)' (as the proof would be infinite)

Source

Stephen Read (Thinking About Logic [1995], Ch.2)

Book Reference

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.44