6 - Model-Theoretic Aspects

Summary

We argue here that Tarski’s conception of “the mathematical” is paradigmatic for model theory, moving foward from Tarski’s work into contemporary practice. The question of when a piece of natural language mathematics has a natural syntax or a natural logic is considered, also in the context of Shelah’sPresentation Theorem. The possibility of laying down a methodology providing a mathematically direct conceptualisation of mathematical content is argued for. The seocnd order logic vs set theory debate is considered, especially focussing on previous attempts to separate the two. Symbiosis is discussed at length as providing a solution to the problem of the entaglement of second order logic with set theory.