  In layered superconductors with small interlayer Josephson coupling
vortex-antivortex phase fluctuations characteristic of quasi two-dimensional
(2D) Kosterlitz-Thouless (KT) behavior are expected to be observable at some
energy scale $T_d$. While in the 2D case $T_d$ is uniquely identified by the KT
temperature $T_{KT}$ where the universal value of the superfluid density is
reached, we show that in a generic anisotropic 3D system $T_d$ is controlled by
the vortex-core energy, and can be significantly larger than the 2D scale
$T_{KT}$. These results are discussed in relation to recent experiments in
cuprate superconductors, which represent a typical experimental realization of
layered anisotropic superconductors.
