Related papers: Corrigendum to "Model Theory of Fields with Virtua…
This paper has been withdrawn by the author(s), due a mistake of factor 1/2.
This paper has been withdrawn due to a crucial theoretical and experimental error.
This paper has been withdrawn by the author(s) and included into the new version of "An extension theorem for separately holomorphic functions with singularities", math.CV/0104089.
This paper is withdrawn. We found a mistake in Lemma 4.1
In our paper arXiv:1310.6289, we stated that acylindrical hyperbolicity of a group is invariant under commensurability up to finite kernels. Unfortunately, the proof of this fact contained a gap. The goal of this erratum is to point out the…
For each $n\in\mathbb{N}$, let $[n]\phi$ mean "the sentence $\phi$ is true in all $\Sigma_{n+1}$-correct transitive sets." Assuming G\"odel's axiom $V = L$, we prove the following graded variant of Solovay's completeness theorem: the set of…
We prove the decidability of the elementary theory of a free group.
This paper has been withdrawn because Proposition 2.2 (c) is false. This invalids the main results of section 2 and 3. We thank A. Canonaco for pointing us the error.
This paper has been withdrawn by the author, due to an error in Proposition 2.2.
This paper has been withdrawn by the authors. We have discovered an error in the evaluation of the diagram, which invalidates our conclusion.
This paper has been withdrawn by the author due to a crucial error in equation (51).
There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.
This paper has been withdrawn by the author, due to a significant error in section 4.3.1.
This paper has been withdrawn by the author due to an error.
This paper was withdrawn by the authors. Lemma 5.1 is wrong.
The paper has been withdrawn by the author due to a crucial error.
We prove that no infinite field is definable in the theory of the free group
This paper has been withdrawn by the authors due to an error in the main theorem.
A theorem of Myasnikov and Roman'kov says that any verbally closed subgroup of a finitely generated free group is a retract. We prove that all free (and many virtually free) verbally closed subgroups are retracts in any finitely generated…
This paper has been withdrawn by the author: it was a too preliminary version.