acl, selinux etc can give you a much fine-grained control but you will have to look at a complicated tutorial to do that. The following can be done easily, your /tmp folder already behaves in a fashion similar to your requirements.
Suppose the directory is /home/descentspb/share. Just do
Now if user1 creates a file, only user1 will be able to remove it. All users can create their own files.
chmod 1777 /home/descentspb/share
I understand that this is not exactly your requirement. You don't even want the creator to be able to remove a file.
EDIT: note that the owner of /home/descentspb/share can delete all files in it. If you don't want this, make root its owner.
sudo chown root /home/descentspb/share
sudo chmod 1777 /home/descentspb/share