Given that 0<|a|<|b|<|1|, is it possible to manipulate this to get an inequality in the form: $$|a|> |expression(b)|$$ , such that:
- $expression(b)$ is an expression that contains the variable b
- the $expression(b)$ contains no mentions of a
- everything is an element of the reals
Your task is possible, but only if you allow for the expression of $b$ to always equal $0$. You see, $|a|$ can be arbitrarily small, so any expression $p(b)$ satisfying $|a|>|p(b)|$ for all $a\ne 0$ must be equal to $0$. Think about it: if $p(b)\ne 0$ for some $b$, then we can choose $a=\frac{p(b)}{2}$ that doesn't satisfy your equation.
The only possible general solution is $p(b)=0$ for all $b$, so if you require the expression to actually contain $b$ in it, you can just artificially inject $b$ into the expression by defining $p(b)=b-b$.