Does there exist a very weak axiomatic theory of arithmeticweaker than (but possibly a subtheory of) Robinson's theory Qwhich can be interpreted in the first order fragment of Frege logic? If so, what are the axioms of such a theory? By "the first order fragment of Frege logic" I mean the system discussed on pages 251252 of the book "One Hundred years of Russell's Paradox" (edited by Godehard Link).
