Higher Set Theory - Classical and Ordinal Computability

Exercise Sheet 11 due on Tuesday, 5 July 2011

25. Show that ≡ is (a) symmetric,

(b) reflexive.

(4 points)

26. Show in SO

(a)]enumerate

(P, ≡, ◀⊧ (Inf^{ZFC})

\begin{matrix}27. \\ 28. \end{matrix} (ℙ, ≡, ◀⊧ (F ound^{ZFC})

(4 points)

29. Show in SO

(a)]enumerateF orevery

(≡, ◀)-formula ϕ(P, ≡, ◀⊧ (Rep_{ϕ}^{ZFC}). {30. \atop 31.} The axiom scheme (Rep^{ZFC}) implies the scheme(Sep^{mathsfZF C)}.

(4 points) (4 points)