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Martin’s axiom does not imply that every two ℕ1-dense sets of reals are isomorphic

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Abstract

Assuming the consistency of ZFC we prove the claim in the title by showing the consistency with ZFC of: There exists a set of realsA such that every function fromA toA is order preserving on an uncountable set. We prove related results among which is the consistency with ZFC of: Every function from the reals into the reals is monotonic on an uncountable set.

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References

  1. U. Avraham, M. Rubin and S. Shelah, in preparation.

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Author notes

  1. Uri Avraham

    Present address: Department of Mathematics, Dartmouth College, 03755, Hanover, NH, USA

Authors and Affiliations

  1. The Hebrew University of Jerusalem, Jerusalem, Israel

    Uri Avraham & Saharon Shelah

Authors
  1. Uri Avraham
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  2. Saharon Shelah
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Additional information

I would like to thank the United States-Israel Binational Science Foundation for supporting this research by a grant.

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Avraham, U., Shelah, S. Martin’s axiom does not imply that every two ℕ1-dense sets of reals are isomorphic. Israel J. Math. 38, 161–176 (1981). https://doi.org/10.1007/BF02761858

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  • DOI: https://doi.org/10.1007/BF02761858

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