We present new results from near-infrared spectroscopy with Keck/MOSFIRE of [OIII]-selected galaxies at $zsim3.2$. With our $H$ and $K$-band spectra, we investigate the interstellar medium (ISM) conditions, such as ionization states and gas metallicities. [OIII] emitters at $zsim3.2$ show a typical gas metallicity of $mathrm{12+log(O/H) = 8.07pm0.07}$ at $mathrm{log(M_*/M_odot) sim 9.0-9.2}$ and $mathrm{12+log(O/H) = 8.31pm0.04}$ at $mathrm{log(M_*/M_odot) sim 9.7-10.2}$ when using the empirical calibration method. We compare the [OIII] emitters at $zsim3.2$ with UV-selected galaxies and Ly$alpha$ emitters at the same epoch and find that the [OIII]-based selection does not appear to show any systematic bias in the selection of star-forming galaxies. Moreover, comparing with star-forming galaxies at $zsim2$ from literature, our samples show similar ionization parameters and gas metallicities as those obtained by the previous studies using the same calibration method. We find no strong redshift evolution in the ISM conditions between $zsim3.2$ and $zsim2$. Considering that the star formation rates at a fixed stellar mass also do not significantly change between the two epochs, our results support the idea that the stellar mass is the primary quantity to describe the evolutionary stages of individual galaxies at $z>2$.
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