# The far side of the cube

## TL;DR

This paper introduces the most general game-semantic model by relaxing all combinatorial constraints of traditional PCF models, providing a foundational framework that encompasses all other models and offers insights into the core of game semantics.

## Contribution

It presents a unified, extremal game model that relaxes all constraints, serving as a fundamental and simplified portal to understanding complex game semantics.

## Key findings

- The model generalizes all existing game models.
- It simplifies the understanding of game semantics.
- Provides a baseline for future semantic models.

## Abstract

Game-semantic models usually start from the core model of the prototypical language PCF, which is characterised by a range of combinatorial constraints on the shape of plays. Relaxing each such constraint usually corresponds to the introduction of a new language operation, a feature of game semantics commonly known as the `Abramsky Cube'. In this presentation we relax all such combinatorial constraints, resulting in the most general game model, in which all the other game models live. This is perhaps the simplest set up in which to understand game semantics, so it should serve as a portal to the other, more complex, game models in the literature. It might also be interesting in its own right, as an extremal instance of the game-semantic paradigm.