Theoretical Oxygen Compression

This is all theoretical of course, but I am curious to see what the possible answer might be. So here it goes....

If you took a gallon of liquid oxygen (231 cubic inches for simplicity).....and you attached a balloon to the oxygen container and opened the valve.....(this is a magical balloon ;-)) the balloon would begin to expand as the oxygen warmed up and turned to gas. So lets say you let the balloon fill all the way up till there is no more liquid oxygen in the container. You remove the balloon from the valve and tie it off so that none of the oxygen escapes.

Now like I said, this is a magical balloon. The balloon also happens to be the worlds most sophisticated compressor. You turn the balloon on and it begins to shrink and as it shrinks, the gas begins to compress.

Now, initially the gallon of liquid oxygen occupied 231 cubic inches. What would happen to the oxygen if it was compressed beyond 231 cubic inches. Let's say down to 200 cubic inches and beyond....say down to 1 cubic inch? Would the gas inside at some point have turned into a liquid or would it just be some seriously compressed gas? What would happen to the oxygen once it was compressed down to 1 cubic inch?

I understand that there is no magical balloon and that we probably don't have the technology to compress 231 cubic inches of liquid down to 1 cubic inch.....but if we DID have the technology, what would happen?