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Katětov order on Borel ideals

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Abstract

We study the Katětov order on Borel ideals. We prove two structural theorems (dichotomies), one for Borel ideals, the other for analytic P-ideals. We isolate nine important Borel ideals and study the Katětov order among them. We also present a list of fundamental open problems concerning the Katětov order on Borel ideals.

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Acknowledgements

The results of the paper were obtained in 2004. They were announced in [12] and included in D. Meza’s Ph.D. thesis [28] written under my supervision. Only now they apper in print with full proofs. I wish to thank D. Chodounský, O. Guzmán and D. Meza for commenting on preliminary versions of the paper. In particular, I would like to thank D. Chodounský for plotting the diagram out for me.

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  1. Instituto de Matemáticas, UNAM, Área de la Investigación Científica Circuito Exterior, Ciudad Universitaria, Coyoacán, 04510, Mexico, D.F., Mexico

    Michael Hrušák

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  1. Michael Hrušák
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Correspondence to Michael Hrušák.

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The research was partially supported by PAPIIT Grant IN108014 and CONACYT Grant 177758.

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Hrušák, M. Katětov order on Borel ideals. Arch. Math. Logic 56, 831–847 (2017). https://doi.org/10.1007/s00153-017-0543-x

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