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  1. Functoroids and ptykoids.J. R. G. Catlow - 1995 - Archive for Mathematical Logic 33 (6):413-425.
    A type of first-order analogues of ptykes, namely ‘ptykoids’, are introduced, and bounds are found for the ptykoids of level 1 and 2 which can be proved to be ptykoids in Peano arithmetic. This gives rise toΠ 3 0 andΠ 4 0 independence results.
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