Is there a way to make a PDF field uneditable once filled?

Hi. I'm trying to post a fillable sign-up form PDF online to be shared with a small group. Is there any way to set the field properties such that a field becomes uneditable after beeing filled out? The idea is that we are posting a "first come, first served" sign up sheet. So I want to make it so that once someone has signed up for an item, someone else can't erase their name and put their own in its place.

Thanks in advance!