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I put some things on User blog:C7X/Drafts

I'm able to delete blog posts if you want one of yours to be deleted (IDK if there's a setting that lets everyone delete their own blog posts)

List of some stability-related ordinals and properties: User:C7X/Stability

How to make light theme for the logo: Paste .wds-community-header__wordmark{filter:invert(100%);} into your common.css

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)

• For a class $$A$$, $$\mathcal P(A)$$ denotes the class of subsets of $$A$$
• $$0\in\mathbb{N}$$
• $$\varphi$$ is Veblen varphi
• Function $$\psi$$=Buchholz psi ($$\psi$$ is $$\psi_0$$)
• Function $$\theta$$=Feferman theta
• Function $$\vartheta$$=Weiermann vartheta
• $$-$$ is relative complement between sets
• $$\subset$$ is strict subset
• $$\subseteq$$ is subset or equal
• $$|x|$$ is cardinality of $$x$$
• For a cardinal $$\kappa$$, a set $$x$$ has "$$\kappa$$-many elements" if $$|x|=\kappa$$
• Let $$S$$ be a set of Booleans. $$\bigwedge S$$ and $$\bigvee S$$ are conjunction and disjunction of all (possibly vacuous) members of the set (can be thought of as $$\forall(t\in S)(t)$$ and $$\exists(t\in S)(t)$$, however formulae are objects in the metatheory), for example, $$\bigvee\{\textrm{False,True,False}\}=\textrm{True}$$)
• "Kripke-Platek set theory" includes the axiom of infinity
• Quantification:
• For example, $$\exists(\beta>\alpha)(\cdots)$$ means $$\exists(\beta)(\alpha\in\beta\land\cdots)$$

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 satisfies 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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