arXiv subjects

Andreas Baudisch

Publications and source records attributed to Andreas Baudisch.

7 recordsLinked to original sources

arXiv2022

Nilpotent Group-Counterexamples to Zilbers Conjecture

We construct uncountably categorical 3-nilpotent groups of exponent p > 3. They are not one-based and do not allow the interpretation of an infinite field. Therefore they are counterexamples to Zilbers Conjecture. First 2-nilpotent new uncoutably categorical groups were contructed in [3]. Here we use the method of the additive Collapse developed in [5]. Essentially we work with 3-nilpotent graded Lie algebras over the field with p elements.

math.LO↗

arXiv2017

A model theoretic study of right-angled buildings

We study the model theory of countable right-angled buildings with infinite residues. For every Coxeter graph we obtain a complete theory with a natural axiomatisation, which is $ω$-stable and equational. Furthermore, we provide sharp lower and upper bounds for its degree of ampleness, computed exclusively in terms of the associated Coxeter graph. This generalises and provides an alternative treatment of the free pseudospace.

math.LO↗

arXiv2014

Neostability properties of Fraisse limits of 2-nilpotent groups of exponent p > 2

We amalgamate finite 2-nilpotent groups G of exponent p > 2, where G' is contained in a subgroup of the center, generated by n elements. We get Fraisse limits D(n) with superstable elementary theories of SU-rank 1. D(1) is Felgner's extra special p-group.

math.LO↗

arXiv2014

Free amalgamation and automorphism groups

Let L be a countable elementary language, N be a Fraisse limit. We consider free amalgamation for L-structures where L is arbitrary. If free amalgamation for finitely generated substructures exits in N, then it is a stationary independece relation in the sense of K.Tent and M.Ziegler [TZ12b]. Therefore Aut(N) is universal for Aut(M) for all substructures M of N. This follows by a result of I.Müller [Mue13] We show that c-nilpotent graded Lie algebras over a finite field and c-nilpotent groups of exponent p (c < p) with extra predicates for a central Lazard series provide examples. We replace the proof in [Bau04] of the amalgamation of c-nilpotent graded Lie algebras over a field by a correct one.

math.LO↗

arXiv2013

Ample Hierarchy

The ample hierarchy of geometries of stables theories is strict. We generalise the construction of the free pseudospace to higher dimensions and show that the n-dimensional free pseudospace is ω-stable n-ample yet not (n+1)-ample. In particular, the free pseudospace is not 3-ample. A thorough study of forking is conducted and an explicit description of canonical bases is exhibited.

math.LO↗

arXiv2006

On fields and colours

We exhibit a simplified version of the construction of a field of Morley rank p with a predicate of rank p-1, extracting the main ideas for the construction from previous papers and refining the arguments. Moreover, an explicit axiomatization is given, and ranks are computed.

math.LO↗

arXiv1997

Closures in $\aleph_0$-categorical bilinear maps

Alternating bilinear maps with few relations allow to define a combinatorial closure similarly as in [2]. For the $\aleph_0$-categorical case we show that this closure is part of the algebraic closure.

math.RA↗