The boundary of determinacy within second order arithmetic.
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The boundary of determinacy within second order arithmetic.
How much determinacy can be proved without using uncountable objects?
Antonio Montalbán. U. of Chicago. The boundary of determinacy within second
order ...
The boundary of determinacy within second order arithmetic. Antonio Montalb´an. U. of Chicago
(with Richard A. Shore) Berkeley, CA, March 2011
Special session in honor of Leo Harrington.
Antonio Montalb´ an. U. of Chicago
The boundary of determinacy within second order arithmetic.
The Question
How much determinacy can be proved without using uncountable objects?
Antonio Montalb´ an. U. of Chicago
The boundary of determinacy within second order arithmetic.
Determinacy Fix a set A ⊆ ω ω . Player I Player II
a0
a2 a1
a3
··· ···
let ¯a = (a0 , a1 , a2 , a3 , ...)
Player I wins is ¯a ∈ A, and Player II wins if ¯a ∈ ω ω \ A. A strategy is a function s : ω
