Solovay rank-comparison game
= Solovay rank-comparison game
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In the Solovay rank-comparison game, Players I and II produce $x,y\in\omega^\omega$; ill-founded codes lose before ranks are compared, and among well-order codes the prescribed inequality between $\lVert x\rVert$ and $\lVert y\rVert$ decides the winner. No strategy for Player I can uniformly produce a well-order code at least as long as every code produced by Player II.