κ

and

λ

(κ^{+})^{λ} = κ^{λ} \cdot κ^{+} = max {κ^{λ}, κ^{+}} .

Equivalently,

ℵ_{α + 1}^{ℵ_{β}} = ℵ_{α}^{ℵ_{β}} \cdot ℵ_{α + 1} .

Solved by gpt-5.6-sol high.

ii

Solution

Fn (X, Y, κ)

p : X ⇀ Y

such that

∣ dom p ∣ < κ .

It is ordered by reverse inclusion:

p \leq q

exactly when

p \supseteq q

, so a stronger condition supplies more values.

Solved by gpt-5.6-sol high.

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