A function of data and parameter with a parameter-free law is a pivot

In usual notations, if a quantity $\phi(T,\theta)$ exists, whose distribution is independent of $\theta$, then which of the following statements are correct? (1) $\phi(T,\theta)$ is called a confidence interval. (2) $\phi(T,\theta)$ is a pivotal quantity. (3) $\phi(T,\theta)$ can be used to define $(1-\alpha)100\%$ confidence interval for $\theta$.