Microreductions: Set Theoretical Form

Abstract

It has long been recognized that in a nontrivial reduction of T₂ to T₁, T₁ must be supplemented with a set of connecting sentences in order to make possible the explanation of the law-sentences of T₂. In the case of microreductions, it has been recognized that some of these connecting sentences should be some kind of identities between the elements in Dom₂ and elements in Dom₁ However, most investigators have also thought that at least some of the connecting sentences are certain types of law-sentences, and for this reason these connecting sentences are often called “bridge laws”. I will eventually argue that all connecting sentences must be identities; some will be thing-identities and some will be attribute-identities. However, in this chapter I will develop, as far as is possible, conditions for microreductions in set theoretical terms.