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In layered superconductors with small interlayer Josephson couplingvortex-antivortex phase fluctuations characteristic of quasi two-dimensional(2D) Kosterlitz-Thouless (KT) behavior are expected to be observable at someenergy scale $T_d$. While in the 2D case $T_d$ is uniquely identified by the KTtemperature $T_{KT}$ where the universal value of the superfluid density isreached, we show that in a generic anisotropic 3D system $T_d$ is controlled bythe vortex-core energy, and can be significantly larger than the 2D scale$T_{KT}$. These results are discussed in relation to recent experiments incuprate superconductors, which represent a typical experimental realization oflayered anisotropic superconductors.Comment: Final version, to appear on Physical Review Letter

Kosterlitz-Thouless Behavior in Layered Superconductors: The Role of the Vortex Core Energy