ɪnðə lˈæŋɡwɪdʒ ʌv vˈɑːn nˈuːmən bˈɜːneɪz ɡˈɜːdəl sˈɛt θˈiəɹi ˌɛnbˌiːdʒˈiː ænd mˈɔːɹs kˈɛli sˈɛt θˈiəɹi, ðɪ ˈæksɪəm ʌv ɡlˈoʊbəl tʃˈɔɪs kæn biː stˈeɪɾᵻd dᵻɹˈɛktli , ænd ɪz ɪkwˈɪvələnt tə vˈɛɹiəs ˈʌðɚ stˈeɪtmənts:
In the language of von Neumann–Bernays–Gödel set theory (NBG) and Morse–Kelley set theory, the axiom of global choice can be stated directly , and is equivalent to various other statements: