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Galvin’s “Racing Pawns” Game and a Well-Ordering of Trees

Available Formats:
Electronic ISBN: 978-1-4704-0729-2
Product Code: MEMO/53/316.E
List Price: $23.00 MAA Member Price:$20.70
AMS Member Price: $13.80 Click above image for expanded view Galvin’s “Racing Pawns” Game and a Well-Ordering of Trees Available Formats:  Electronic ISBN: 978-1-4704-0729-2 Product Code: MEMO/53/316.E  List Price:$23.00 MAA Member Price: $20.70 AMS Member Price:$13.80
• Book Details

Memoirs of the American Mathematical Society
Volume: 531985; 63 pp
MSC: Primary 03; Secondary 05; 06; 90;

• Chapters
• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 531985; 63 pp
MSC: Primary 03; Secondary 05; 06; 90;
• Chapters
• 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
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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