The Yellow Cake

by Roslanowski and Shelah. [RoSh:686]
Proc American Math Soc, 2001
We consider the following property: (*) For every function f:R x R ---> R there are functions g^0_n,g^1_n:R ---> R (for n< omega) such that (for all x,y in R)(f(x,y)= sum_{n< omega}g^0_n(x)g^1_n(y)) . We show that, despite some expectation suggested by [Sh:675], (*) does not imply MA(sigma-centered). Next, we introduce cardinal characteristics of the continuum responsible for the failure of (*) .

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