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

44 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

Access to Document

10.1007/BF02761858

Cite this

@article{1e69b88e25134bcd94944c91a13ee155,

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

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.",

author = "Uri Avraham and Saharon Shelah",

year = "1981",

month = mar,

doi = "10.1007/BF02761858",

language = "אנגלית",

volume = "38",

pages = "161--176",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "1-2",

}

TY - JOUR

T1 - Martin's axiom does not imply that every two ℕ1-dense sets of reals are isomorphic

AU - Avraham, Uri

AU - Shelah, Saharon

PY - 1981/3

Y1 - 1981/3

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/51249183594

U2 - 10.1007/BF02761858

DO - 10.1007/BF02761858

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:51249183594

SN - 0021-2172

VL - 38

SP - 161

EP - 176

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

IS - 1-2

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this