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Towers on trees
We show that (under MA) for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="German c"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="fraktur">c</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathfrak {c}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> many dense sets in Laver forcing <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper L"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">L</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">\mathbb {L}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> …