Abstract
Answering a question of Harrington, we show that there exists a proper forcing notion, which adds a minimal real η ∈ ∏ i > ω n i ∗ \eta \in \prod _{i>\omega } n^*_i , which is eventually different from any old real in ∏ i > ω n i ∗ \prod _{i>\omega } n^*_i , where the sequence ⟨ n i ∗ ∣ i > ω ⟩ \langle n^*_i \mid i>\omega \rangle grows slowly.
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