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Gap structure after forcing with a coherent Souslin tree

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Abstract

We investigate the effect after forcing with a coherent Souslin tree on the gap structure of the class of coherent Aronszajn trees ordered by embeddability. We shall show, assuming the relativized version PFA(S) of the proper forcing axiom, that the Souslin tree S forces that the class of Aronszajn trees ordered by the embeddability relation is universal for linear orders of cardinality at most\({\aleph_1}\).

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Authors and Affiliations

  1. Centro de Ciencias Matematicas, Universidad Nacional Autonomade Mexico, Antigua Carretera a Patzcuaro 8701, CP 58089, Morelia, Michocán, Mexico

    Carlos Martinez-Ranero

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  1. Carlos Martinez-Ranero
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Correspondence to Carlos Martinez-Ranero.

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I gratefully acknowledge support from Conacyt Grant 99047.

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Martinez-Ranero, C. Gap structure after forcing with a coherent Souslin tree. Arch. Math. Logic 52, 435–447 (2013). https://doi.org/10.1007/s00153-013-0323-1

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  • DOI: https://doi.org/10.1007/s00153-013-0323-1

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