ABSTRACT
We briefly indicate here how one can create a “mirror” of pre-mathematical logic within mathematics (indeed within algebra). What results is a subject called mathematical logic (also referred to as formal logic). A special place in mathematical logic is played by models/model theory which we shall explain below in some detail. In particular we will discuss models of ZFC itself (and hence of mathematics itself); this concept of model is entirely different from that of metamodels in the chapter on metamodels. In the discussion of models of ZFC we will introduce what one can call formalized set theory. We will discuss models of other (simpler) theories as well such as the theory of Peano arithmetic.
