they will not allow us
Article IV § 2 states: No acts or activities taking place while the present Treaty is in force shall constitute a basis for asserting, supporting or denying a claim to territorial sovereignty in Antarctica. No new claim, or enlargement of an existing claim, to territorial sovereignty shall be asserted while the present Treaty is in force
That only applies to countries that has signed the treaty. Which we won't. Anyway, non of the nations have the right to deny our claim either. Also, if they disagree with our decision they can't do anything since according to the treaty, no military activity is allowed on Antarctica. I don't see what could possibly stop us? (except for money)