A note on the expressive power of linear orders

Abstract

This article shows that there exist two particular linear orders such that first-order logic with these two linear orders has the same expressive power as first-order logic with the Bit-predicate FO(Bit). As a corollary we obtain that there also exists a built-in permutation such that first-order logic with a linear order and this permutation is as expressive as FO(Bit).

Cited by in corpus (2)

• k variables are needed to define k-Clique in first-order logic
• On the strictness of the quantifier structure hierarchy in first-order logic