Uniform n-place functions on T\subseteq ds(α)

Mathematics – Logic

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

Scientific paper

In this paper the Erdos-Rado theorem is generalized to the class of well founded trees. We define an equivalence relation on the class rs(infty)^{< aleph_0} (finite sequences of decreasing sequences of ordinals) with aleph_0 equivalence classes, and for n< omega a notion of n-end-uniformity for a colouring of rs(infty)^{< aleph_0} with mu colours. We then show that for every ordinal alpha, n< omega and cardinal mu there is an ordinal lambda so that for any colouring c of T=rs(lambda)^{< aleph_0} with mu colours, T contains S isomorphic to rs(alpha) so that c rest S^{< aleph_0} is n-end uniform. For c with domain T^n this is equivalent to finding S subseteq T isomorphic to rs(alpha) so that c upharpoonright S^{n} depends only on the equivalence class of the defined relation, so in particular T-> (rs(alpha))^n_{mu, aleph_0} . We also draw a conclusion on colourings of n-tuples from a scattered linear order.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Uniform n-place functions on T\subseteq ds(α) 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 Uniform n-place functions on T\subseteq ds(α), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Uniform n-place functions on T\subseteq ds(α) will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-222164

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.