2026/05/02 by Mark Carney · 3 voices
#math.LO #cs.LO
Odrzywołek defined a system Exp-Minus-Log (EML) that reduces all elementary functions over complex numbers down to a constant `1', and a single two place function E(α, β) = exp(α) - log(β). This paper shows that in this system, equivalent to Chow's EL numbers, every EML-expressible number is computable. We go on to prove that the canonical example of a non-computable real, Chaitin's ΩU, is inexpressible in EML. This gives a formal inexpressibility theorem for this system.