The Pierce Expansion Problem

I just posted one of my oldest open math problems to Math Overflow. Let's see if anyone can come up with a new idea for attacking this problem, which I thought of back in 1978, and only a little progress has been made in 36 years.

Just What Russia Needs

The Templeton Foundation, not content with its corrupting influence on American science, is branching out to encourage more theology in Russia.

What wonderful news! If there's anything that Russia needs now, it's more theology. I wonder what we can look forward to. Perhaps a "natural law" justification for putting gays in prison, or for the takeover of Crimea.