User:TGReddy/TGR's Playground/tOCF

Definition

 * \( \alpha \vartriangleleft A \) is true iff for all functions \( f : \alpha \rightarrow \alpha \), there exists \( \kappa \in A \) that is closed under \( f \)


 * \( A_{n} = \text{enum}(A) \)
 * \( L(A) = \{ \text{sup}(B) : B \subset A \} \)
 * \( r(A,B) = L(A) \cap B \)


 * \( T \left[ \cdots \; \begin{matrix} 0 \\ 0 \end{matrix} \right] = L(Reg) \)
 * \( T \left[ \cdots \; \begin{matrix} n+1 \\ 0 \end{matrix} \right] = r( T \left[ \cdots \; \begin{matrix} n \\ 0 \end{matrix} \right], \{ a : a = T \left[ \cdots \; \begin{matrix} n \\ 0 \end{matrix} \right]_{a} \} ) \)
 * \( T \left[ \cdots \; \begin{matrix} n+1 & 0 \\ \left[ \cdots \; \begin{matrix} m+1 \\ 0 \end{matrix} \right] & \left[ \cdots \; \begin{matrix} m \\ 0 \end{matrix} \right] \end{matrix} \cdots \right] = \{ a : a = T \left[ \cdots \; \begin{matrix} n & a \\ m+1 & m \end{matrix} \cdots \right] \} \)
 * \( T \left[ \cdots \; \begin{matrix} n+1 \\ \left[ \begin{matrix} 1 \\ 1 \end{matrix} \right] \end{matrix} \cdots \right] = \{ a : a \dagger T \left[ \cdots \; \begin{matrix} n \\ \left[ \begin{matrix} 1 \\ 1 \end{matrix} \right] \end{matrix} \cdots \right] \} \)