**Diamond principle** $♢$ (TeX `\diamondsuit`) is the statement
*what?...*
Variants:
$♢_κ$ or $♢(κ)$ is the statement “There exist sets $(S_α\|α < κ)$,
$S_α ⊆ α$ ($α < κ$) such that for any $X ∈ κ$ the set $\{α\|X ∩ α =
S_α\}$ is
<a href="index.php?title=Mahlo_set&action=edit&redlink=1" class="new" title="Mahlo set (page does not exist)">Mahlo</a>”
introduced in
{% cite Jensen1969 Ketonen1974 %}
Results:
- $♢$ holds in the [](Constructible%20universe.md)
$L$.
- If $κ$ is
<a href="Ethereal" class="mw-redirect" title="Ethereal">ethereal</a>
and $2^\underset{\smile}{κ} = κ$, then $♢_κ$ holds (where
$2^\underset{\smile}{κ} = \bigcup \{ 2^α \| α < κ \}$ is the
weak power of
$κ$).{% cite Ketonen1974 %}
- If $κ$ is
[ineffable](Ineffable.md "Ineffable"),
weakly ineffable or
<a href="Subtle" class="mw-redirect" title="Subtle">subtle</a>,
then $♢_κ$
holds.{% cite Jensen1969 Ketonen1974 %}
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