Stability of op-amps: "Oscillations if phase = 180° and loop gain > 1" question
However, it is just as often stated that an circuit will oscillate if, at the frequency at which the phase = -180°, the loop gain is greater than or equal to 1. How is this reconciled with Equation 1?


If the loop gain is greater than 1 with a phase shift of -180°, if the op-amp remains linear then in principle you could produce an oscillator with a constantly increasing output amplitude.

But of course the output amplitude can't increase indefinitely. There will be some nonlinearity in the op-amp (or feedback network) response that limits the output amplitude. For example, the op-amp could enter saturation mode operation.

Often this will effectively limit the op-amp gain so that \$\beta A_0\$ is reduced to 1, and you have the Barkhausen criterion fulfilled after all.