Completeness Theorems, Representation Theorems: What's the Difference?
David Makinson · London School of Economics and Political Science Research Online (London School of Economics and Political Science) · 2007
Abstract: Most areas of logic can be approached either semantically or syntactically. Typically, the approaches are linked through a completeness or representation theorem. The two kinds of theorem serve a similar purpose, yet there also seems to be some residual distinction between them. In what respects do they differ, and how important are the differences? Can we have one without the other? We discuss these questions, with examples from a variety of different logical systems. 1. Introduction: Syntax