Galvin's Conjecture and Weakly Precipitous Ideals

We show that if κ is a Ramsey cardinal then every fine countably complete normal ideal concentrating on a set in V_κ (hence every normal ideal on ω₁) satisfies a weak form of precipitousness. As an application we show that Ramsey cardinals can be used instead of Woodin cardinals and stationary tower forcing to push through the Raghavan-Todorčević proof of a longstanding conjecture of Galvin: if a Ramsey cardinal exists then for any uncountable set of reals X and any coloring c of [X]² with finitely many colors, there is a subspace of X homeomorphic to the rationals on which c takes on at most two colors. Finally, we use work of Donder and Levinsky to show that this partition theorem for uncountable sets of reals can hold in a generic extension of Gödel's L, and therefore does not imply the existence of 0^♯.