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STRUCTURE OF SUMMABLE TALL IDEALS UNDER KATĚTOV ORDER
- Part of
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- Journal:
- The Journal of Symbolic Logic , First View
- Published online by Cambridge University Press:
- 20 April 2023, pp. 1-27
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- Article
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We show that Katětov and Rudin–Blass orders on summable tall ideals coincide. We prove that Katětov order on summable tall ideals is Galois–Tukey equivalent to
$(\omega ^\omega ,\le ^*)$. It follows that Katětov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that 
${l_\infty }$ is Borel bireducible to an equivalence relation induced by Katětov order on summable tall ideals.
