# A partial order where all monotone maps are definable

Martin Goldstern; Saharon Shelah

Fundamenta Mathematicae (1997)

- Volume: 152, Issue: 3, page 255-265
- ISSN: 0016-2736

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topGoldstern, Martin, and Shelah, Saharon. "A partial order where all monotone maps are definable." Fundamenta Mathematicae 152.3 (1997): 255-265. <http://eudml.org/doc/212210>.

@article{Goldstern1997,

abstract = {It is consistent that there is a partial order (P,≤) of size $ℵ_1$ such that every monotone function f:P → P is first order definable in (P,≤).},

author = {Goldstern, Martin, Shelah, Saharon},

journal = {Fundamenta Mathematicae},

keywords = {partial ordering; monotone mapping; definability; relative consistency; adding Cohen reals to a model of },

language = {eng},

number = {3},

pages = {255-265},

title = {A partial order where all monotone maps are definable},

url = {http://eudml.org/doc/212210},

volume = {152},

year = {1997},

}

TY - JOUR

AU - Goldstern, Martin

AU - Shelah, Saharon

TI - A partial order where all monotone maps are definable

JO - Fundamenta Mathematicae

PY - 1997

VL - 152

IS - 3

SP - 255

EP - 265

AB - It is consistent that there is a partial order (P,≤) of size $ℵ_1$ such that every monotone function f:P → P is first order definable in (P,≤).

LA - eng

KW - partial ordering; monotone mapping; definability; relative consistency; adding Cohen reals to a model of

UR - http://eudml.org/doc/212210

ER -

## References

top- [KS] H. Kaiser and N. Sauer, Order polynomially complete lattices, Algebra Universalis 130 (1993), 171-176. Zbl0784.06004
- [Sh 128] S. Shelah, Uncountable constructions for B.A., e.c. groups and Banach spaces, Israel J. Math. 51 (1985), 273-297.
- [Sh 136] S. Shelah, Constructions of many complicated uncountable structures and Boolean algebras, Israel J. Math. 45 (1983), 100-146.

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