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# C7X

I put most things on User blog:C7X/Drafts List of some stable ordinals (ordered by increasing size of first ordinal satisfying the condition): User:C7X/Stability

Triple xi $$\xi^{\!\!\!\!\!\!\phantom{!}\phantom{!}\phantom{!}^\zeta}$$

Inline/small tree $$\substack{\circ&-&\circ&-&\circ \\ \vert&&\vert&& \\ \circ&&\circ&& \\ \vert&&&& \\ \circ&&&&}$$ text

## Conventions

I use these conventions on most of my things (unless otherwise specified)

• $$\varphi$$ is Veblen varphi
• $$\psi$$=Buchholz psi ($$\psi$$ is $$\psi_0$$)
• $$\theta$$=Feferman theta
• $$\vartheta$$=Weiermann vartheta
• $$-$$ is relative complement between sets
• $$\subset$$ is strict subset
• $$\subseteq$$ is subset or equal
• $$f^n$$ is iteration of the function $$f$$
• $$|x|$$ is cardinality of $$x$$
• $$\land S$$ and $$\lor S$$ are conjunction and disjunction of all (possibly vacuous) members of the set (can be defined as $$\forall(t\in S)(t)$$ and $$\exists(t\in S)(t)$$), where S is a set of Booleans (for example, $$\lor\{\textrm{False,True,False}\}=\textrm{True}$$)

I use ZFC+Generalized Continuum Hypothesis+$$\exists\text{A proper class of inaccessibles}$$

### Types of OCFs

If a function is called some variant of the symbol $$\psi$$, it probably refers to something that acts similarly to Buchholz psi (it may or may not use regular subscripts, what's important is that $$\psi(\varepsilon_0+1)\neq\omega^{\varepsilon_0+1}$$)

If a function is called some variant of the symbol $$\vartheta$$, it probably refers to something that acts similarly to Weiermann vartheta (it uses an equality similar to $$\vartheta(\varepsilon_0+1)=\omega^{\varepsilon_0+1}$$)

If a function is called some variant of the symbol $$\theta$$, it probably refers to something that acts similarly to Feferman theta

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