On Pillay's conjecture in the general case
Let M be an arbitrary o-minimal structure. Let G be a definably compact, definably connected, abelian definable group of dimension n. Here we compute: (i) the new intrinsic o-minimal fundamental group of G; (ii) for each k>0, the k-torsion subgroups...
mehr
|
Let M be an arbitrary o-minimal structure. Let G be a definably compact, definably connected, abelian definable group of dimension n. Here we compute: (i) the new intrinsic o-minimal fundamental group of G; (ii) for each k>0, the k-torsion subgroups of G; (iii) the o-minimal cohomology algebra over Q of G. As a corollary we obtain a new uniform proof of Pillay's conjecture, an o-minimal analogue of Hilbert's fifth problem, relating definably compact groups to compact real Lie groups, extending the proof already known in o-minimal expansions of ordered fields.
|
On freely generated E-subrings
In this paper we prove, without assuming Schanuel's conjecture, that the E-subring generated by a real number not definable without parameters in the real exponential field is freely generated. We also obtain a similar result for the complex...
mehr
|
In this paper we prove, without assuming Schanuel's conjecture, that the E-subring generated by a real number not definable without parameters in the real exponential field is freely generated. We also obtain a similar result for the complex exponential field. © 2008 Elsevier B.V. All rights reserved.
|
Comparing ℂ and zilber's exponential fields: Zero sets of exponential polynomials
We continue the research programme of comparing the complex exponential with Zilbers̈ exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for using analytic function...
mehr
|
We continue the research programme of comparing the complex exponential with Zilbers̈ exponential. For the latter, we prove, using diophantine geometry, various properties about zero sets of exponential functions, proved for using analytic function theory, for example, the Identity Theorem.
|
Generic solutions of equations with iterated exponentials
We study solutions of exponential polynomials over the complex field. Assuming Schanuel’s Conjecture we prove that certain polynomials of the form p(z, ez, eez, eeez) = 0 have generic solutions in C.
mehr
|
We study solutions of exponential polynomials over the complex field. Assuming Schanuel’s Conjecture we prove that certain polynomials of the form p(z, ez, eez, eeez) = 0 have generic solutions in C.
|
