ZFC independence and subset sum

TL;DR

This paper explores the independence of certain combinatorial structures related to subset sum from ZFC axioms, linking set theory and computational complexity to reveal foundational limitations.

Contribution

It demonstrates that specific combinatorial structures associated with subset sum are independent of ZFC, highlighting fundamental limitations in mathematical provability.

Findings

Existence of structures is ZFC-independent

Connections between set theory and subset sum complexity

Insights into foundational limits of mathematics

Abstract

We study recursively defined functions associated with directed graphs on the k dimensional nonnegative integral lattice. The existence of certain combinatorial structures associated with these function classes are shown to be independent of the ZFC axioms of mathematics. These structures, in a natural way, give rise to sets of instances to the subset sum problem. We use this connection to make some observations about ZFC independence and the subset sum problem.