# Talk:Ehrenfeucht–Fraïssé game

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Field:  Foundations, logic, and set theory

"4. Duplicator picks whichever of a2 or b2 Spoiler did not pick." is phrased infelicitously, since it suggests Duplicator's pick is an already known specific individual of its structure -- but it isn't until Duplicator has moved. Rather, the earlier language that described Duplicator's side of the first move-pair should be echoed: "If Spoiler picked a2 from A then Duplicator picks some b2 from B not equal to any previous move from B, and contrariwise if Spoiler picked b2 from B then Duplicator picks some a2 from A not equal to any previous move from A." (N. Shum-Ish 06:13, 21 June 2007 (UTC))

## Finite vocabulary

The number of relation symbols must be finite. Otherwise one can construct elementarily equivalent structures on which Spoiler wins a single-round EF game. — Preceding unsigned comment added by 2A02:8109:9900:2AC:DC74:2492:D105:8B21 (talk) 21:48, 4 February 2014 (UTC)

## Definition or Example?

The definition section starts "Suppose that we are given two structures \mathfrak{A} and \mathfrak{B}, each with no function symbols...". This implies that function symbols are to be excluded, by definition, from any instance of the Ehrenfeucht–Fraïssé game. Is this the case? Or should this section be named "Example" rather than "Definition"? Jim Bowery (talk) 17:40, 7 April 2015 (UTC)