Does the Partition Principle imply the Axiom of Choice?

Theorem 1.1: Con(ZF) implies Con(ZF + PP + ACwo + $\neg$AC). Theorem 1.2: over every countable transitive model $V$ of ZFC there are a set forcing and a transitive symmetric submodel $W$ with $V\subseteq W\subseteq V[G]$, the same ordinals, $W\models$ ZF + PP + ACwo + $\neg$AC, and no new countable sequences of elements of $V$. The construction makes every non-wellorderable image of a fixed set bijective with it and uses Ryan-Smith's local-to-global reduction. Remarks draw consequences for the dual Cantor-Schroeder-Bernstein principle and the Weak Partition Principle. It does not settle whether the Weak Partition Principle implies AC or PP, nor other cardinal-comparison principles beyond those remarks.

Theorem 1.1: Con(ZF) implies Con(ZF + PP + ACwo + $\neg$AC). Theorem 1.2: over every countable transitive model $V$ of ZFC there are a set forcing and a transitive symmetric submodel $W$ with $V\subseteq W\subseteq V[G]$, the same ordinals, $W\models$ ZF + PP + ACwo + $\neg$AC, and no new countable sequences of elements of $V$. The construction makes every non-wellorderable image of a fixed set bijective with it and uses Ryan-Smith's local-to-global reduction. Remarks draw consequences for the dual Cantor-Schroeder-Bernstein principle and the Weak Partition Principle. It does not settle whether the Weak Partition Principle implies AC or PP, nor other cardinal-comparison principles beyond those remarks.