Answer by Ashutosh for Building Sets/Functions by Playing Games
What you describe above is called a Cantor scheme in a polish space X. If one also requires that the closure of $N_v$ is a subset of $N_u$ whenever $u < v$, we get a point in X along each branch of...
View ArticleAnswer by Carl Mummert for Building Sets/Functions by Playing Games
The use of the "winning" condition is to ensure that the overall construction has the properties we want. For example, in the game in the original question, Player 1 chooses "left" or "right" at each...
View ArticleAnswer by tzy for Building Sets/Functions by Playing Games
In the set $A$ produced by assuming the axiom of choice, why is the game not determined when obviously one player has to win eventually because the sequence produced has to be in $A$ or outside $A$?...
View ArticleAnswer by tzy for Building Sets/Functions by Playing Games
The Evolutionary Biology thing is interesting. Has determinacy been helpfun in theoretical computer science (AI) then, especially with regards to the Church-Turing thesis?In an infinite games, Adam...
View ArticleAnswer by Joel David Hamkins for Building Sets/Functions by Playing Games
I will give two explanations for why games crop up so fruitfully, one explanation from mathematics and the other arising from evolutionary biology. The mathematical explanation for why games crop up in...
View ArticleBuilding Sets/Functions by Playing Games
I have sat in lectures on set theory and I have seen the use of games cropping up in many places. I don't really understand what was going on and how useful games are in set theory, but here I have a...
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