All Questions
Tagged with combinatorial-game-theory set-theory
9 questions
27
votes
1
answer
2k
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Are Conway's combinatorial games the "monster model" of any familiar theory?
This is related to this question about a "mother of all" groups, and so seemed like it'd fit in better at MO than MSE.
If I understand the answer to that question correctly, the surreal numbers have ...
- 4,907
25
votes
4
answers
2k
views
The Chocolatier's game: can the Glutton win with a restricted form of strategy?
I have a question about the Chocolatier's game, which I had
introduced in my recent answer to a question of Richard
Stanley.
To recap the game quickly, the Chocolatier offers up at each stage
a finite ...
- 236k
24
votes
2
answers
1k
views
What is the complexity of the winning condition in infinite Hex? In particular, is infinite Hex a Borel game?
Consider the game of infinite Hex, where two players Red and Blue alternately place their stones on the infinite hex grid, each aiming to create a winning configuration.
Red wins after infinite play, ...
- 236k
9
votes
2
answers
691
views
Choosing subsets of $\mathbb R$ of cardinality $\frak c$, who wins?
Consider the following infinite game: two players, I and II, are alternating and choosing a descending sequence of subsets of $\mathbb R$ of cardinality $\frak c$, so I chooses a set $A_1\subseteq\...
- 28.2k
7
votes
2
answers
736
views
Sets as Combinatorial Games
Just a few days ago my seemingly eternal and recurrent fascination for Conway's combinatorial game theory (CGT) & surreal numbers had a recrudescence, so I grabbed this excellent survey, and began ...
- 7,853
5
votes
1
answer
436
views
Uniform strategy on Kastanas' game
I think my question applies to most games, but for the sake of concreteness, I shall consider one specific game in this question. We consider the game posed by Ilias Kastanas in his paper On the ...
- 1,442
5
votes
1
answer
503
views
What ordinal corresponds to the T(3)?
Let's play a game. You start with the ordinal $\alpha$ and I start with the empty sequence. Each turn, you decrease your ordinal, and I add a tree (where each node can have one of three labels), ...
- 6,403
5
votes
1
answer
1k
views
Set theory / Formal logic of Baba is You
''Baba is You'' is a recent puzzle game in which the player builds a set of rules by pushing squares with words written on them. If we leave aside the combinatorial difficulty of how to move the ...
- 5,146
5
votes
0
answers
396
views
Why is this transfinite game not determined?
This question originates from the paper On the Axiom of Determinateness by Jan Mycielski, section 7. Given a set $X$ and an ordinal $\alpha$, the author defines a transfinite game of length $\alpha$ ...
- 907