catur-ārūpya brahmālokas; also 四無色界 and see 四空定. The four immaterial or formless heavens, arūpa-dhātu, above the eighteen brahmālokas: (1) 空無邊處 ākāśānantyāyatana, also termed 虛空 處 the state or heaven of boundless space; (2) 識無邊處 vijñānanāntyāyatana, of boundless knowledge; (3) 無所有處 ākiñcanyāyatana, of nothing, or nonexistence; (4) 非想非非想處 naivasanjñānasañjnāyatana, also styled 非有想非無想 the state of neither thinking nor not thinking (which may resemble a state of intuition). Existence in the first state lasts 20, 000 great kalpas, increasing respectively to 40, 000, 60, 000 and 80, 000 in the other three.

A Dictionary of Chinese Buddhist Terms, William Edward Soothill and Lewis Hodous

四空處 [py] sì kōngchù [wg] ssu k'ung-ch'u [ko] 사공처 sa gongch'ŏ [ja] シクウショ shi kūsho ||| The 'four locations in the formless realm.' Four spheres of existence within the formless realm. Also written siwushi 四無色. Those who practice the four formless concentrations are born here. See 四無色.

[Dictionary References] Naka511d [Credit] cmuller(entry) cwittern(py)

又名四無色，或無色界，即空無邊處、識無邊處、無所有處、非想非非想處，乃修四空處定的人所得的正報，因此四處的眾生於五蘊中無色蘊，只有受想行識的四蘊，亦即無物質的色身，而只有微妙的精神存在，亦無依報的國土宮殿，故名無色界，或四空處。
 

陳義孝編, 竺摩法師鑑定, 《佛學常見辭彙》