This work removes the set-theoretic hypothesis of CH and explores minimal extensions, indicating novel properties.
We build on a 1990 paper of Bukovský and Copláková-Hartová. First, we remove the hypothesis of CH from one of their minimality results. Then, using a measurable cardinal, we show that there is a | ₂V|= ₁ -minimal extension that is not a | ₃V|= ₁ -extension, answering the first of their questions.
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Maxwell Levine (2025) studied this question.
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