## FANDOM

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$$\omega^{CK}_1$$ is the ordinal strength of Turing Machines, and the smallest non-recursive ordinal. What about $$\omega^{CK}_2$$ or $$\omega^{CK}_n$$? If $$\omega^{CK}_1$$ is the limit of A(0), B(0), C(0), D(0), and so on, where A, B, C, D... are normal functions, is the limit of $$A(\omega^{CK}_1+1)$$, $$B(\omega^{CK}_1+1)$$, $$C(\omega^{CK}_1+1)$$, $$D(\omega^{CK}_1+1)$$... $$\omega^{CK}_2$$ or it is smaller. Also is the limit of oracle machines with access to the halting problem $$\omega^{CK}_2$$?