However, the examples given above are not functionally complete in this stronger sense because it is not possible to write a nullary function, i . e . a constant expression, in terms of " F " if " F " itself does not contain at least one nullary function.
32.
Further study by Pearce Paul Creasman has concluded that the temple was " functionally complete . " She could, hence, have possibly ruled for 6 to 20 more months after the inscription date to achieve these levels of completion, thus starting her 9th regnal year around the interval of IV Akhet / I Peret when her husband died ( since she assumed Siptah's reign as her own ) or perhaps longer before Setnakhte's rule began.
33.
As for the axiomatization, Th ( " A " ) is finitely axiomatizable for any finite model " A " in a finite language, so let me just assume that you fix any finite complete axiomatization " Z n " of Th ( "'Z "'/ " n " "'Z "') in the ( functionally complete, in this case ) language of rings ( the particular choice of the axioms does not matter, since the equivalence of two finitely axiomatized theories is a \ Sigma ^ 0 _ 1-statement, and is thus verifiable already in Robinson arithmetic whenever it is true ).
