Strategy stealing, the axiom of determinacy, and why it's incompatible with the axiom of choice. #SoME3
Resources to learn more and other interesting notes:
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Chomp:
Play online: https://www.math.ucla.edu/~tom/Games/chomp.html
Wikipedia article: https://en.wikipedia.org/wiki/Chomp
List of known best first moves: https://sites.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/chompc.html
Also check out chapter 18 in the book "Winning Ways for Your Mathematical Plays"
Zermelo's Theorem: https://en.wikipedia.org/wiki/Zermelo%27s_theorem_(game_theory)
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The Axiom of Determinacy:
Wikipedia article: https://en.wikipedia.org/wiki/Axiom_of_determinacy
Borel Determinacy Theorem: https://en.wikipedia.org/wiki/Borel_determinacy_theorem
The argument in the video is essentially given as Proposition 28.1 in the book The Higher Infinite by Akihiro Kanamori, but it is stated in more complicated terms. You can also find some discussion of it at this link: https://mathoverflow.net/questions/49709/boolean-prime-ideal-theorem-versus-the-axiom-of-determinacy
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The Axiom of Choice:
Wikipedia article: https://en.wikipedia.org/wiki/Axiom_of_choice
Banach-Tarski Paradox: https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
Vsauce Video on Banach-Tarski Paradox: https://www.youtube.com/watch?v=s86-Z-CbaHA
Corrections: