  The best way of appreciating the nature of Tarski’s theory of logical consequence and how it constitutes an application of the methods of Tarskian semantics is to see how it applies to a particular formal language of a simple structure, of a kind that Tarski seems to have primarily in mind in his paper of 1936. We will choose a simple language of this kind for a fragment of elementary arithmetic. This language, LAr, can be given this quick description: