# [Existential–universal real sentences in the counting hierarchy](etr-counting-hierarchy.pdf)

**Author:** OpenAI

**Date:** October 4, 2026

## Citation

```bibtex
@misc{OAI:Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026,
  author = {{OpenAI}},
  title = {{Existential--universal real sentences in the counting hierarchy}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026/etr-counting-hierarchy.pdf}{OAI:Existential-universal-real-sentences-in-the-counting-hierarchy-October-4-2026}},
  year = {2026}
}
```