  We present high-resolution ALMA observations of the C$^{18}$O, $^{13}$CO and
$^{12}$CO $J$=1-0 isotopologues in 3 nearby ultra-luminous infrared galaxies
(ULIRGS; Arp 220, IRAS 13120-5453, IRAS 17208-0014) and 1 nearby post-merger
galaxy (NGC 2623). In all 4 systems, we measure high $^{12}$CO/C$^{18}$O and
$^{12}$CO/$^{13}$CO integrated line ratios while the $^{13}$CO/C$^{18}$O ratio
is observed to be extremely low in comparison to typical star-forming disks,
supporting previous work. We investigate whether these unusual line ratios are
due to dynamical effects, astrochemistry within the gas, or nucleosynthesis in
stars. Assuming both lines are optically thin, low $^{13}$CO/C$^{18}$O values
suggest that C$^{18}$O is more abundant than $^{13}$CO in the interstellar
medium of these systems. A plausible explanation is that local ULIRGs and their
progeny have an excess in massive star formation; in other words, they are
producing a top-heavy stellar initial mass function.
