TABLE OF CONTENTS Page Introduction and Preliminaries 1 Galvin*s Original Game, the Restricted Game, and the Relations *R and =R 4 The Explicit Strategy for Finite Trees and the Definitions of E and F 13 The Explicit Strategy for Infinite Trees and the Characterization -A _i of R and =R in Terms of E and F 25 -A _L The Structure of the E and F Sequences 31 The Relationship Between F (x) and Rank(x) 44 The Main Theorem: Order Types Under 54 Epilogue: Two Variants of Galvin's Game 60 iii
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