4 problems

Let $f_1,\ldots,f_t$ be relatively prime real polynomials of positive degrees with respect to $x_{f+1},\ldots,x_r$, and let $x=(x_1,\ldots,x_f)$. Let $D(x)$ be a generalized discri…

Quantifier-elimination conjecture. The following are equivalent:

Let $K$ be a field. Say that $K$ has almost quantifier elimination if every formula $\phi(x)$, with $x=(x_1,\ldots,x_m)$, is equivalent to a formula $\exists y\,\theta(x,y)$, where…

Let $R=\Z[t]$ and $X=\N$. Define … where each $g_{\alpha(t)}$ is interpreted by … with $g_{\alpha(t)}(x)=0$ when $\alpha(t)=0$. Quantifier-elimination conjecture. Every…