A Partial Order Where All Monotone Maps Are Definable
逻辑
2016-09-07 v1
摘要
It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support iteration of Cohen forcing. The main points is that (1) all monotone functions from P to P will (essentially) have countable range (this uses a Delta-system argument) and (2) that all countable subsets of P will be first order definable, so we have to code these countable sets into the partial order. Amalgamation of finite structures plays an essential role.
引用
@article{arxiv.math/9707202,
title = {A Partial Order Where All Monotone Maps Are Definable},
author = {Martin Goldstern and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9707202},
year = {2016}
}
备注
This is paper number GoSh:554 in Shelah's list. The paper is to appear in Fundamenta Mathematicae.