The Noetherian–Pfaffian counting o-minimality conjecture

Let $\mathbb R_{\mathrm{LN},\mathrm{PF}}$ be the structure generated by the larger class of Noetherian and Pfaffian functions considered in the paper. Noetherian–Pfaffian counting o-minimality conjecture. The structure $\mathbb R_{\mathrm{LN},\mathrm{PF}}$ is $\#$-o-minimal. The paper proves effective o-minimality for this structure, which provides progress toward—but does not resolve—the stronger counting o-minimality assertion.