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

Abstract

top
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,≤).

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.