145. The Fourth Island

Two native inhabitants A and B of this island stated:

A: We are both liars, and this island is called Maya.

B: At least one of us is a liar, and this island is not Maya.

Can we assert that the fourth island is indeed called Maya?
145. Islander A is a known liar, as the statement made by him cannot belong to a knight. If B is a knight, then from the statement made by him it follows that the fourth island is not the Maya Island. If, however, B is a liar, then the first part of the statement made by A is true. But the entire statement of A is false (since A is a liar), so its second part must also be false. Therefore, in this case, the fourth island is also not the Maya Island.