48 research outputs found

    Definable maximal cofinitary groups of intermediate size

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    Using almost disjoint coding, we show that for each 1<M<N<ω1<M<N<\omega consistently d=ag=ℵM<c=ℵN\mathfrak{d}=\mathfrak{a}_g=\aleph_M<\mathfrak{c}=\aleph_N, where ag=ℵM\mathfrak{a}_g=\aleph_M is witnessed by a Π21\Pi^1_2 maximal cofinitary group.Comment: 22 page

    Definability of maximal cofinitary groups

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    We present a proof of a result, previously announced by the second author, that there is a closed (even Π10\Pi^0_1) set generating an FσF_\sigma (even Σ20\Sigma^0_2) maximal cofinitary group (short, mcg) which is isomorphic to a free group. In this isomorphism class, this is the lowest possible definitional complexity of an mcg.Comment: This work is part of the first authors thesi
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