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Generic embeddings and the failure of box

Generic embeddings and the failure of box

We prove that if {<inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="a subset-of-or-equal-to kappa Superscript plus Baseline vertical-bar"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>⊆</mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>κ</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">a \subseteq {\kappa ^ + }|</mml:annotation> </mml:semantics> </mml:math> </inline-formula> order type of <italic>a</italic> is a cardinal} is …