Low-temperature specific heat (SH) is measured on the 1111-type CaFe_{0.88}Co_{0.12}AsF single crystals under different magnetic fields. A clear SH jump with the height Delta C/T|_Tc = 10.4 mJ/mol K^2 was observed at the superconducting transition temperature T_c. The electronic SH coefficient Deltagamma (B) increases linearly with the field below 5 T and a kink is observed around 5 T, indicating a multi-gap feature in the present system. Such a sign is also reflected in the Tc-B data. A detailed analysis shows that this behavior can be interpreted in terms of a two-gap scenario with the ratio Delta_L=Delta_S = 2:8-4:5.
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