Weak Monadic Second Order Theory of Successor is not Element-recurive
Let L SIS be the set of formulas expressible in a week monadic second order logic using only the predicates [x =y+1] and [x E z]. Bucci and Elgot [3,4] have shown that the truth of sentences in L SIS (under the standard interpretation < N, successor > with second order variables interpreted as...
| Main Author: | |
|---|---|
| Published: |
2023
|
| Online Access: | https://hdl.handle.net/1721.1/148867 |
| Summary: | Let L SIS be the set of formulas expressible in a week monadic second order logic using only the predicates [x =y+1] and [x E z]. Bucci and Elgot [3,4] have shown that the truth of sentences in L SIS (under the standard interpretation < N, successor > with second order variables interpreted as ranging over finite sets) is decidable. We refer to the true sentences in L SIS as WSIS. We shall prove that WSIS is not elementary-recursive in the sense of Kalmar. In fact, we claim a stronger result: |
|---|