Any behaviour of the Mitchell Ordering of Normal Measures Is Possible

Details Any behaviour of the Mitchell Ordering of Normal Measures Is Possible Any behaviour of the Mitchell Ordering of Normal Measures Is Possible

1993-12-03

arxiv.org/abs/math/9312203v1

Mathematics

Logic

Scientific paper

Let $U_0,U_1$ be two normal measures on $\kappa .$ We say that $U_0$ is in the Mitchell ordering less then $U_1,$ $U_0\vartriangleleft U_1,$ if $U_0 \in Ult(V,U_1) .$ The ordering is well-known to be transitive and well-founded. It has been an open problem to find a model where the Mitchell ordering embeds the four-element poset $|\; | .$ We show that in the Kunen-Paris extension all well-founded posets are embeddable. Hence there is no structural restriction on the Mitchell ordering. Moreover we show that it is possible to have two $vartriangleleft$-incomparable measures that extend in a generic extension into two $\vartriangleleft$-comparable measures.

Affiliated with

Also associated with

No associations

Rating

Any behaviour of the Mitchell Ordering of Normal Measures Is Possible 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 Any behaviour of the Mitchell Ordering of Normal Measures Is Possible, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Any behaviour of the Mitchell Ordering of Normal Measures Is Possible will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-467820