Inexpressibility in Exp-Minus-Log
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918478233993216 |
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| author | Carney, Mark |
| author_facet | Carney, Mark |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01636 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inexpressibility in Exp-Minus-Log Carney, Mark Logic Logic in Computer Science 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. |
| title | Inexpressibility in Exp-Minus-Log |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2605.01636 |