Finite-variable logics do not have weak Beth definability property
arXiv:1409.5059 · doi:10.1007/978-3-319-15368-1_4
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 (Ildikó Sain and András 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.