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

Uri Avraham; Saharon Shelah

doi:10.1007/BF02761858

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

Uri Avraham^*, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

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 reals A such that every function from A to A 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.

Original language	English
Pages (from-to)	161-176
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	38
Issue number	1-2
DOIs	https://doi.org/10.1007/BF02761858
State	Published - Mar 1981

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

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