Independence Structures in Set Theory
Michiel van Lambalgen

Abstract:
The axioms for "independent choices" presented in van Lambalgen [1992] are 
strengthened here, so that they can be seen as introducing a new type of 
indiscernibles in set theory. The resulting system allows for the construction 
of natural inner models. The article is organised as follows. Section 1 
introduces the axioms, some preliminary lemmas are proved and the relation 
with the axiom of choice is investigated. Section 0 gives a philosophical 
motivation for the axioms; the reader who is not interested in such matters 
can skip this part. In section 2 we compare the structure introduced by the 
axioms, here called an independence structure, with two constructions from 
model theory, indiscernibles and minimal sets. Section 3 contains the 
construction of inner models, while section 4 presents some concluding 
philosophical remarks.