Introduction. In this work we discuss recursive mappings between theories which preserve deducibility, negation and implication. Roughly, we prove that any two axiomatizable theories containing a small fragment of arithmetic—this can be stated precisely—are "isomorphic" by a primitive recursive function mapping sentences onto sentences which also preserves deducibility, negation and implication...

Two elements in an oriented matroid are inseparable if they have either the same sign in every signed circuit containing them both or opposite signs in every signed circuit containing them both. Two elements of a matroid are adjacent if there is no M(K4)-minor using them both, and in which they correspond to a matching of K4. We prove that two elements e, { of an oriented matroid are inseparabl...