Nice Bdawg, but correct me if I am wrong, and I say this on 3 beers

Pressure and Temperature are the changing variables, not Volume. This is not a piston in a car or a compressor or a ballon (etc.), the volume of the Fermentor stays the same. We need to use Gay-Lussac's law, and see that when the temperature drops, so does the pressure, 'drawing' in (based on the atmospheric pressure outside of the Fermentor) the outside air (O2/N2/Misc).
Gay-Lussac's, Charles' and Boyles' laws are all based on the Ideal Gas law you stated above. Keep one constant, while the other two have relationships where they vary.
P1*T2=P2*T1
You are showing a Fermentor changing in volume above. I may be completely wrong. One needs some more steps to correlate the change in pressure to the addition of volume.