Finite-variable logics do not have weak beth definability property

Hajnal Andréka

István Németi

pp. 125-133

in: Arnold Koslow, Arthur Buchsbaum (eds), The road to universal logic II, Basel, Birkhäuser, 2015

Abstract

We prove that n-variable logics do not have the weak Beth definability property, for all (ngeq 3). This was known for n = 3 (Ildikó Sain and András Simon), and for (ngeq 5) (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 (ngeq 3). The case for n = 2 is left open.

Cited authors

Hodkinson Ian