Micromathematics

[Ignacio Añón]

Shipman wrote:

""What I am really asking is “how useful would an oracle for Th(V_i) be?”
for i=0,1,…9.""

You can set a Polynomial in several variables, with integer coeficients,
and define upper bounds for its diophantine solvability in nonnegative
integers...

This shows clearly that for Th(V_i), oracles will always find simpler
solutions, impossible to reach in i <= i -1, while any "minimal" Cohen
model of ZFC, might also make the polynomial redundant in i <= i - 1...

The best paper I've seen about this unknown limit is:

On a diophantine representation of the predicate of provability. M. Carl.

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