Mathematics and Set Theory:

Interpreting Set Theory in Discrete Mathematics: Boolean Relation Theory

Wqo theory = well quasi ordering theory, is a branch of combinatorics which has proved to be a fertile source of deep metamathematical pheneomena. In wqo theory, one freely uses some overtly set theoretic arguments. They are definitely noticeable, although they come fairly early in the interpretation hierarchy. Way before, say, ZFC. A qo (quasi order) is a reflexive transitive relation (A,£). A...

The reality of mathematics and the case of set theory

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.

The Infinite as Method in Set Theory and Mathematics

This article address the historical emergence of the infinite in set theory, and how we are to take the infinite in and out of mathematics.The first section discusses the emergence of the infinite as a matter of method in set theory. The second section discusses the infinite in and out of mathematics, and how it is to be taken.

Second Order Logic, Set Theory and Foundations of Mathematics

The question, whether second order logic is a better foundation for mathematics than set theory, is addressed. The main difference between second order logic and set theory is that set theory builds up a transfinite cumulative hierarchy while second order logic stays within one application of the power sets. It is argued that in many ways this difference is illusory. More importantly, it is arg...