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ArticleOriginal scientific text

Title

A partial order where all monotone maps are definable

Authors 1, 2, 3

Affiliations

  1. Technische Universität, Wiedner Hauptstrasse 8-10/118.2, A-1040 Wien, Austria
  2. Current address: Mathematik WE 2 Freie Universität Arnimallee 3 D-14195 Berlin
  3. Hebrew University of Jerusalem, Givat Ram, 91094 Jerusalem, Israel

Abstract

It is consistent that there is a partial order (P,≤) of size ℵ1 such that every monotone function f:P → P is first order definable in (P,≤).

Bibliography

  1. [KS] H. Kaiser and N. Sauer, Order polynomially complete lattices, Algebra Universalis 130 (1993), 171-176.
  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.
Fundamenta Mathematicae
1997/152/3
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Pages:
255-265
Main language of publication
English
Received
1996-02-26
Accepted
1996-06-24
Published
1997
Exact and natural sciences