However, it could also be the reaction if your company is approaching or is currently in a busy season and needs the additional staff, or it's experiencing unusual circumstances, like a hiring freeze, which would prevent it from replacing you entirely.
A Professional Greeting. Your letter should be addressed to your boss. There's a good chance that this letter will merely end up in a file in HR, but it starts with your boss. Assuming this is someone with whom you work reasonably close with on a daily basis, it doesn't have to be super stiff and formal. Specific and professional is the right tone here.