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The results stated in this paper first appeared in Crossley's D.Phil. thesis (Oxford. 1963), The ‘proof’ given there of theorem 2.2.(iii) was incorrect and the proof here is entirely due to Schütte.
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Crossley, J.N., Schütte, K. Non-uniqueness at ω2 in Kleene'sO . Arch math Logik 9, 95–101 (1966). https://doi.org/10.1007/BF01973029
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DOI: https://doi.org/10.1007/BF01973029