A new proof that analytic sets are Ramsey

We give a direct mathematical proof of the Mathias-Silver theorem that every analytic set is Ramsey. ?

[1]  Fred Galvin,et al.  Borel sets and Ramsey's theorem , 1973, Journal of Symbolic Logic.

[2]  Jack Howard Silver,et al.  Every analytic set is Ramsey , 1970, Journal of Symbolic Logic.