Prisoner's Hat (Infinity)

A countably infinite line of prisoners $P_1, P_2, P_3, \ldots$ each wears a red or blue hat; the colors are assigned arbitrarily and unknown to the prisoners. Everyone faces the same direction so that prisoner $P_i$ can see the hats of all prisoners $P_j$ with $j > i$, but not his own hat or the hats of $P_1, \ldots, P_{i-1}$.

Starting with $P_1$, then $P_2$, and so on, each prisoner must guess the color of his own hat; if he is wrong, he is killed. The prisoners may agree on a strategy beforehand, but once in line no prisoner can hear anything the others say or learn anything about their guesses or fates. Only his view of the hats ahead of him is available.

Is there a strategy that guarantees that only finitely many prisoners are killed, whatever the hat assignment?