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Galvin’s “racing pawns” game and a well-ordering of trees

About this Title

S. B. Grantham

Publication: Memoirs of the American Mathematical Society
Publication Year 1985: Volume 53, Number 316
ISBNs: 978-0-8218-2317-0 (print); 978-1-4704-0729-2 (online)
MathSciNet review: 776346
MSC: Primary 04A20; Secondary 03E05, 05C05, 06A10, 90D05

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Table of Contents


  • 1. Introduction and preliminaries
  • 2. Galvin’s original game, the restricted game, and the relations $<_R$ and $\equiv _R$
  • 3. The explicit strategy for finite trees and the definitions of $\overset {\rightharpoonup }{E}$ and $\overset {\rightharpoonup }{F}$
  • 4. The explicit strategy for infinite trees and the characterization of $<_R$ and $\equiv _R$ in terms of $\overset {\rightharpoonup }{E}$ and $\overset {\rightharpoonup }{F}$
  • 5. The structure of the $\overset {\rightharpoonup }{E}$ and $\overset {\rightharpoonup }{F}$ sequences
  • 6. The relationship between $\overset {\rightharpoonup }{F}(X)$ and $\operatorname {rank}(X)$
  • 7. The main theorem: Order types under $<_R$
  • 8. Epilogue: Two variants of Galvin’s game