Re: compactness in angels/devil problem

On Fri, 1 Feb 2008 pauldepstein@xxxxxxx wrote:

The literature on the angels-and-devil problem often refers to a
"compactness argument" for passing from conclusions about finite
boards to conclusions about the infinite case. What is this
"compactness argument" and which topology is the compactness concept
being applied to?

The compactness theorem for FOL logic is:

if P can be concluded from an infinite set S of statements,
then P can be concluded from a finite subset of S.

Formally. Within an FOL, if S is an infinite set of statements
and S |- P, then there's a finite F subset S with F |- P.

.

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