Elementary equivalence of infinite-dimensional classical groups

Details Elementary equivalence of infinite-dimensional classical groups Elementary equivalence of infinite-dimensional classical groups

2011-12-12

arxiv.org/abs/1112.2652v1

Mathematics

Logic

A prepublication preprint of a paper published in 2000

Scientific paper

Let D be a division ring such that the number of conjugacy classes in the multiplicative group D^* is equal to the power of D^*. Suppose that H(V) is the group GL(V) or PGL(V), where V is an infinite-dimensional vector space over D. We prove, in particular, that, uniformly in dim(V) and D, the first-order theory of H(V) is mutually syntactically interpretable with the theory of the two-sorted structure (whose only relations are the division ring operations on D) in the second-order logic with quantification over arbitrary relations of power <= dim(V). A certain analogue of this results is proved for the groups the collinear groups GammaL(V) and PGammaL(V). These results imply criteria of elementary equivalence for infinite-dimensional classical groups of types H=GammaL, PGammaL, GL, PGL over division rings, and solve, for these groups, a problem posed by Felgner. It follows from the criteria that if H(V_1), H(V_2) are elementarily equivalent, then the cardinals dim(V_1) and dim(V_2) are second order equivalent as sets.

Affiliated with

Also associated with

No associations

Rating

Elementary equivalence of infinite-dimensional classical groups 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 Elementary equivalence of infinite-dimensional classical groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Elementary equivalence of infinite-dimensional classical groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-709485