Inexpressibility in Exp-Minus-Log

Mark Carney

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arXiv · 2605.01636

Inexpressibility in Exp-Minus-Log

Mark Carney

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Abstract

Odrzywo\l{}ek 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 $E(\alpha, \beta) = \exp(\alpha) - \log(\beta)$. 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 $\Omega_U$, is inexpressible in EML. This gives a formal inexpressibility theorem for this system.

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BibTeX RIS

Mark Carney. 2026-05-02. Inexpressibility in Exp-Minus-Log. https://arxiv.org/abs/2605.01636

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