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We have carried out measurements of the pressure dependence to 1.2 GPa of theoxygen isotope effect on $T_c$ in the high-$T_c$ superconductorYBa$_2$Cu$_4$O$_8$ using a clamp cell in a SQUID magnetometer. This compoundlies close to, but just above, the 1/8$^{th}$ doping point where inLa$_{2-x}$Sr$_x$CuO$_4$ marked anomalies in isotope effects occur. Bothisotopes show the same very large pressure dependence of $T_c$ with the resultthat the isotope exponent remains low ($\sim$0.08) but increases slightly withincreasing pressure. This is discussed in terms of stripe suppression, acompeting pseudogap and the effect of superconducting fluctuations.

Pressure dependence of the oxygen isotope effect in YBa$_2$Cu$_4$O$_8$