The Strategic Balance of Games in Logic

TL;DR

This paper explores the interconnectedness of various logical games, demonstrating their strategic similarities and providing translations between their strategies to deepen understanding of logical properties.

Contribution

It introduces the concept of strategic balance in logic, showing how different logical games are related and providing explicit translations of strategies among them.

Findings

Identifies the affinity among evaluation, model-existence, and Ehrenfeucht-Fraisse games.

Provides explicit translations of strategies between these games.

Highlights the concept of strategic balance in logical games.

Abstract

Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to each other and call this phenomenon the strategic balance in logic. In particular, we give explicit translations of strategies from one game to another.