# Quick clarification needed on degeneracy

I need some hints about degeneracy. So, I consider an energy level degenerate if there are two distinct wave functions at that energy.

Then, let's say I have two spin1/2 fermions in a 1D box.

1. Is the ground state double-degenerate? Because I could exchange the spins and get a minus sign because of antisimmetry. Is this correct?
2. the first excited state is 4-degenerate? cause I can excite the spin up and then exchange getting a minus sign, and same for spin down.

If I have spinless bosons instead,

1. Ground state is non degenerate
2. First excited state: non degenerate as well, because if I exchange two bosons nothing happens.