The existence of an extension of
first order logic satisfying both the Compactness Theorem and the Interpolation
Theorem is an open or solved question?

What properties does an "extension of first order logic" need to satisfy (e.g. relativization, isomorphism-invariance, etc.)? With no restrictions, I think uninteresting examples of such logics can be constructed pretty easily.
– Noah SchweberMay 12 '12 at 4:37

3

Also, can you give any background to this problem? I've heard about it before, and I understand it has an interesting history, but that's the extent of my knowledge about it; and I'd be curious to hear anything you might say about it.
– Noah SchweberMay 12 '12 at 4:39