Wedge Sum, Merge and Inconsistency

Abstract

This paper investigates the topological construction of Wedge Sum, with the aim of showing that it can be done mathematically, via a quotient construction, or logically, via Merge. Consistent and Inconsistent versions are given, while noting that the natural outcome of Merging is an inconsistent theory. Finally it is observed that algebraic constructions can also be treated via Merge, where the extra functionality makes for various triviality and non-triviality results.