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arXiv:2605.01636math.LO

Inexpressibility in Exp-Minus-Log

Mark Carney

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Abstract

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 $Ω_U$, is inexpressible in EML. This gives a formal inexpressibility theorem for this system.

arXiv comments
5 pages
Journal reference
DOI
Subjects
math.LOLogic cs.LOLogic in Computer Science

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