Ehrenfeuct game for First-order logic without equality

From: Anthony WIDJAJA (twidjaja_at_cs.mu.OZ.AU)
Date: 04/21/04 

Date: Wed, 21 Apr 2004 02:58:15 GMT

Hello,

I'm just wondering if someone knows whether there is an EF game for
FO without equality. By this, I mean a tool for proving that two
structures cannot be distinguished by any FO sentence without equality
of quantifier depth at most m, for some positive integer m, but can
possibly be distinguished by a FO sentence of this quantifier depth with
equality.

I'm also wondering if there is a general tool for proving that "a property
is not expressible in FO without equality (but may be expressible in FO
with equality).

Any input will be greatly appreciated.

Thanks in advance,

Anthony

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