How does the Chamber Of Secrets make sense when,?

If Tom Riddle IS Lord Voldemort, and his muggle father was Rom Riddle, that makes Lord Voldemort(Tom Riddle) not 'pure blood' and a 'muggle born'. However the Chamber Of Secrets was created to be rid of all the muggle borns in Hogwarts by Salazar Slytherin, because he thought 'muggle borns' or wizards who were not 'pure blood' were not worthy to study magic. So how can Lord Voldemort be Salazar's heir to open the Chamber Of Secrets to kill all 'muggle borns' when he is one himself?