[FOM] question about the complexity of a sentence

[Rupert McCallum]

In his thesis "The Search for New Axioms" Peter Koellner asserts that the following statement

SPHERE. One cannot take a sphere apart into finitely many boldface Sigma^1_2 pieces, and rearrange them using rigid motons to form a sphere twice the size of the original

is a Sigma^1_3 sentence. I am having trouble seeing this. Can anyone explain to me why it is so?

Dr Rupert McCallum
Lecturer in Mathematics
(02) 9701 4050