Forum:How do you represent the LVO ?/Is There a Non-OCF Notation Surpassing the LVO ?

At 8:50 in the below video the person explaining $$\psi(\Omega^{\Omega^{\Omega}})$$ stated it is the supremum of Veblen notation, but not necessarily $$\varphi(1,0,0,0,\ldots)$$, but instead was Veblen notation nested within each other infinitely.



Unfortunately he never explained how this could be done, so I took an educated guess. First, take $$\varphi(1,0,0,0,\ldots)$$ and represent it by a $$v_0$$, next make the rule that $$v_{n+1}=\varphi(v_n,0,0,0,\ldots)$$. I feel the Large Veblen Ordinal is probably equal to the first fixed point of $$\xi\mapsto v_{\xi}$$; if I am mistaken please correct me and explain a procedure involving a nesting of $$\varphi(1,0,0,0,\ldots)$$ that can create the Large Veblen Ordinal.

In addition, is there an ordinal notation that can surpass $$\psi(\Omega^{\Omega^{\Omega}})$$ without resorting to infinite collapsing functions, and which reaches higher ordinals such as $$\psi(\Omega^{\Omega^{\Omega^{\Omega}}})$$, or $$\psi(\psi_I(0))$$ ? Transfinitary-argument Veblen functions vex me, and so I want to find a simpler alternative.

Comments are appreciated.Edwin Shade (talk) 03:05, November 27, 2017 (UTC)