The uniqueness of the core model

TL;DR

This paper investigates the Jensen-Steel core model in set theory, demonstrating that under certain conditions, its defining properties uniquely determine the model, regardless of the hierarchy used.

Contribution

It establishes conditions under which the core model's properties uniquely identify it, clarifying its foundational role in set theory.

Findings

Abstract properties can uniquely determine the core model.

Different hierarchies may lead to the same core model under certain conditions.

The work clarifies the foundational uniqueness of the Jensen-Steel core model.

Abstract

The Jensen-Steel core model is a canonical inner model which plays a fundamental role in the meta-mathematics of set theory. Its definition depends on exactly which hierarchy of fine-structural models of set theory, premice, one uses. Each such hierarchy involves somewhat arbitrary decisions and working with different hierarchies ostensibly leads to different versions of the core model. We show that in some contexts, abstract properties of the core model uniquely determine it; that is, there is at most one inner model with these properties.