Set Equality in Combinatorial Game Theory

TL;DR

This paper investigates the implications of prioritizing set equality over game equivalence in Combinatorial Game Theory, challenging traditional notions and exploring foundational concepts.

Contribution

It introduces a novel perspective by examining set equality prior to game equivalence, offering new insights into the structure of combinatorial games.

Findings

Reveals how set equality influences the understanding of game equivalence

Provides a new framework for analyzing combinatorial game structures

Challenges traditional assumptions in game theory

Abstract

In Combinatorial Game Theory, the fundamental relation of game equivalence, denoted by $=$, is introduced early on and overrides the notion of set equality. We explore what happens if set equality is given its due before game equivalence is introduced.