Proving Independence of Axioms in Game Theory: A Case Study

[crobertson0308]

I have four axioms and I am stuck trying to prove the independence of these axioms.

Axiom 1: Each game is played by two distinct teams.
Axiom 2: There are at least four teams.
Axiom 3: Exactly six games are played.
Axiom 4: Each distinct team played once against the same team.

I've justified both Ax 4 and 3 are independent but need help justifying the other two axioms

 

[johng1]

Hi,
Here is a set of models that prove the independence. I leave it to you to verify that each is actually a model.

 

[s1foot5]

Would the undefined terms be elements(teams, game)...relation(is, are)?

 

[msalamon]

I need to create three theorems that follow from the four axioms. One theorem I came up with was if there are exactly four teams, then each team plays exactly three games. I'm having trouble coming up with another two. The only path I'm seeing is increasing the number of teams and seeing what happens with the models.

 

[s1foot5]

I need to create three theorems that follow from the four axioms. One theorem I came up with was if there are exactly four teams, then each team plays exactly three games. I'm having trouble coming up with another two. The only path I'm seeing is increasing the number of teams and seeing what happens with the models.

What did you get as the undefined terms?

 

[msalamon]

For the objects: game(s), team(s)
For the relations: is, are, and I wasn't sure of played should be considered a relation or not

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Pardon my typo; of should be if.