English

Finite-variable logics do not have weak Beth definability property

Logic 2016-02-26 v1

Abstract

We prove that n-variable logics do not have the weak Beth definability property, for all n greater than 2. This was known for n=3 (Ildik\'o Sain and Andr\'as Simon), and for n greater than 4 (Ian Hodkinson). Neither of the previous proofs works for n=4. In this paper we settle the case of n=4, and we give a uniform, simpler proof for all n greater than 2. The case for n=2 is still open.

Cite

@article{arxiv.1409.5059,
  title  = {Finite-variable logics do not have weak Beth definability property},
  author = {H. Andréka and I. Németi},
  journal= {arXiv preprint arXiv:1409.5059},
  year   = {2016}
}
R2 v1 2026-06-22T05:59:03.001Z