Pointwise Definable Models of Set Theory

Details Pointwise Definable Models of Set Theory Pointwise Definable Models of Set Theory

2011-05-23

arxiv.org/abs/1105.4597v1

Mathematics

Logic

23 pages

Scientific paper

A pointwise definable model is one in which every object is definable without parameters. In a model of set theory, this property strengthens V=HOD, but is not first-order expressible. Nevertheless, if ZFC is consistent, then there are continuum many pointwise definable models of ZFC. If there is a transitive model of ZFC, then there are continuum many pointwise definable transitive models of ZFC. What is more, every countable model of ZFC has a class forcing extension that is pointwise definable. Indeed, for the main contribution of this article, every countable model of Godel-Bernays set theory has a pointwise definable extension, in which every set and class is first-order definable without parameters.

Affiliated with

Also associated with

No associations

Rating

Pointwise Definable Models of Set Theory does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pointwise Definable Models of Set Theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pointwise Definable Models of Set Theory will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-23198