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  • Rgetar

    I interested in ordinals, and I asked myself: "Why we use \(\omega\),  \(\omega2\), \(\omega^2\), \(\omega^\omega\), \(\epsilon_0\), \(\zeta_0\), \(\phi(3,0)\), \(\Gamma_0\) etc. instead of \(\omega\uparrow\uparrow\uparrow\omega\), \(\omega\uparrow\uparrow\uparrow\uparrow\omega\) etc.?"

    But I realized this doesn't work beyond \(\epsilon_0\) since \(\omega\uparrow\uparrow(\omega+1) = \omega^{\omega\uparrow\uparrow\omega} = \omega^{\epsilon_0} = \epsilon_0 = \omega\uparrow\uparrow\omega\).

    I experimented and created a BEAF-like system, suitable also for ordinals.

    It is family of functions [X]a of ordinal a.


    Let X - sequence of ordinals (or "negative ordinals", i.e. ordinals with "-" sign before them) with separators.

    All zeros we may omit.

    All lef…


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