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SPIDERS is the spectroscopic follow-up effort of the Sloan Digital Sky Survey IV (SDSS-IV) project for the identification of X-ray selected galaxy clusters. We present our catalogue of 2740 visually inspected galaxy clusters as part of the SDSS Data Release 16 (DR16). Here we detail the target selection, our methods for validation of the candidate clusters, performance of the survey, the construction of the final sample, and a full description of what is found in the catalogue. Of the sample, the median number of members per cluster is approximately 10, with 818 having 15 or greater. We find that we are capable of validating over 99 per cent of clusters when five redshifts are obtained below z < 0.3 and when nine redshifts are obtained above z > 0.3. We discuss the improvements in this catalogue's identification of cluster using 33 340 redshifts, with Δ z phot/Δ z spec ∼ 100, over other photometric and spectroscopic surveys, as well as presenting an update to previous (σ– L X) and (σ–λ) relations. Finally, we present our cosmological constraints derived using the velocity dispersion function. [ABSTRACT FROM AUTHOR]

SPIDERS (The SPectroscopic IDentification of eROSITA Sources) is a large spectroscopic programme for X-ray selected galaxy clusters as part of the Sloan Digital Sky Survey-IV (SDSS-IV). We describe the final data set in the context of SDSS Data Release 16 (DR16): the survey overall characteristics, final targeting strategies, achieved completeness, and spectral quality, with special emphasis on its use as a galaxy cluster sample for cosmology applications. SPIDERS now consists of about 27 000 new optical spectra of galaxies selected within 4000 photometric red sequences, each associated with an X-ray source. The excellent spectrograph efficiency and a robust analysis pipeline yield a spectroscopic redshift measurement success rate exceeding 98 per cent, with a median velocity accuracy of 20 km s−1 (at z  = 0.2). Using the catalogue of 2740 X-ray galaxy clusters confirmed with DR16 spectroscopy, we reveal the 3D map of the galaxy cluster distribution in the observable Universe up to z ∼ 0.6. We highlight the homogeneity of the member galaxy spectra among distinct regions of the galaxy cluster phase space. Aided by accurate spectroscopic redshifts and by a model of the sample selection effects, we compute the galaxy cluster X-ray luminosity function and we present its lack of evolution up to z  = 0.6. Finally we discuss the prospects of forthcoming large multiplexed spectroscopic programmes dedicated to follow up the next generation of all-sky X-ray source catalogues. [ABSTRACT FROM AUTHOR]