Assuming OCA_T and MA(σ-linked), every homomorphism from P(N) into a quotient by a countably 80-determined ideal has a continuous lifting on a nonmeager ideal, improving PFA-based results and removing MA for countably generated ideals.
Non-trivial copies of N*
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We show that it is consistent to have regular closed non-clopen copies of $\mathbb N^*$ within $\mathbb N^*$ and a non-trivial self-map of $\mathbb N^*$ even if all autohomeomorphisms of $\mathbb N^*$ are trivial.
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Biba's trick, with applications
Assuming OCA_T and MA(σ-linked), every homomorphism from P(N) into a quotient by a countably 80-determined ideal has a continuous lifting on a nonmeager ideal, improving PFA-based results and removing MA for countably generated ideals.