  In this paper we demonstrate how, using a natural generalization of BCS
theory, superconducting phase coherence manifests itself in phase insensitive
measurements, when there is a smooth evolution of the excitation gap \Delta
from above to below Tc. In this context, we address the underdoped cuprates.
Our premise is that just as Fermi liquid theory is failing above Tc, BCS theory
is failing below. The order parameter \Delta_{sc} is different from the
excitation gap \Delta. Equivalently there is a (pseudo)gap in the excitation
spectrum above Tc which is also present in the underlying normal state of the
superconducting phase, and can be directly inferred from specific heat and
vortex core experiments. At the same time many features of BCS theory, e.g.,
fermionic quasiparticles below Tc, are clearly present. These observations can
be reconciled by a natural extension of BCS theory, which includes finite
center-of-mass momentum pair excitations, in addition to the usual fermionic
quasiparticles. Applying this theory we find that the Bose condensation of
Cooper pairs, which is reflected in \Delta_{sc}, leads to sharp peaks in the
spectral function once $T \le T_c$. These are manifested in ARPES spectra as
well as in specific heat jumps, which become more like the behavior in a
\lambda transition as the pseudogap develops. We end with a discussion of
tunneling experiments and condensation energy issues. Comparison between
theoretical and experimental plots of C_v, and of tunneling and vortex core
spectroscopy measurements is good.
