- published: 19 Jun 2016
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In set theory, a branch of mathematics, determinacy is the study of under what circumstances one or the other player of a game must have a winning strategy, and the consequences of the existence of such strategies.
The first sort of game we shall consider is the two-player game of perfect information of length ω, in which the players play natural numbers.
In this sort of game we consider two players, often named I and II, who take turns playing natural numbers, with I going first. They play "forever"; that is, their plays are indexed by the natural numbers. When they're finished, a predetermined condition decides which player won. This condition need not be specified by any definable rule; it may simply be an arbitrary (infinitely long) lookup table saying who has won given a particular sequence of plays.
More formally, consider a subset A of Baire space; recall that the latter consists of all ω-sequences of natural numbers. Then in the game GA, I plays a natural number a0, then II plays a1, then I plays a2, and so on. Then I wins the game if and only if
Always tried to please everyone else
Instead of pleasing God and myself
Looking for love in all the wrong places
Taking my life, my life through unnecessary cases
But I know
I don't have to be in this mess
Unhappy, frustrated and stressed
So I've learned to live by the simple phrase
And it simply says:
That I've got to
Live for myself and nobody else
See its gonna be me,
God alone
Nobody can judge my soul until he calls me home(X2)
Nobody can judge my soul until he calls me home, home,
home
See I tried to prove my salvation
With required attire
Blinded, satisfied with the outer appearance
We could not see on the inside
My soul was in danger of held fire
See I was stained in the eyes of man
I was being remarked against
oh,ohh
Never really get a chance to start again
Never really get a chance to start again
I am determined to live for him
See I've got to start again,
I've got to start again
oh,ohh
I am, yeah
I am determined to live for Him
See I've got to start again,
I've got to start again
I am determined to live for Him
see I've got to start again,
I've got to start again
Listen
No-one can stop me
I'm going to live for Him
And no-one can hold me down (No)