### arnold beckmann's pages

## Separating intermediate predicate logics of well-founded and dually
well-founded structures by monadic sentences

**File:** PDF-File

**Author:** Arnold Beckmann and Norbert Preining

**Title:** Separating intermediate predicate logics of well-founded and dually
well-founded structures by monadic sentences

**Journal:** J Logic Computation (2015) **25**(3): 527-547

**DOI:** 10.1093/logcom/exu016

**Abstract:**
We consider intermediate predicate logics defined by
fixed well-ordered
(or dually well-ordered) linear Kripke frames with constant domains
where the order-type of the well-order is strictly smaller
than~$\omega^\omega$.
We show that two such logics of different order-type are separated by
a first-order sentence using only one monadic predicate symbol.
Previous results by Minari, Takano and Ono, as well as the second
author,
obtained the same separation but
relied on the use of predicate symbols of unbounded arity.