Is it possible to eradicate a tree in Stardew Valley?

I don't think it's possible to completely eliminate trees from the game, but you might have to wait a while. Some things to check:

• Just wait for the seasons to turn; I believe you may randomly spawn new oak saplings even if there's not a mature oak around to seed it.
• Make sure you didn't overlook the trees in the Forest, which you can also cut down and which also respawn eventually.