### arnold beckmann's pages

## Proving consistency of equational theories in bounded arithmetic

**File:** PDF-File

**Author:** Arnold Beckmann

**Title:** Proving consistency of equational theories in bounded arithmetic

**Journal:** JSL 2002, **67**(1): 279-296

**DOI:** 10.2178/jsl/1190150044

**Abstract:**
We consider equational theories for functions defined via
recursion involving equations between closed terms with natural rules
based on recursive definition of the function symbols.
We show that consistency of such equational theories can be proved in
the weak fragment of arithmetic
S
1
2
.
In particular this solves an open problem formulated by Takeuti.