•Pebble Games: with k pebbles
•Notation: A º1wk B if duplicator wins
•
•Theorem 1. For any two
structures A, B:
•A, B are Lk1w equivalent
iff
•A º1wk B
•Theorem 2. If A, B are finite:
•A, B are FOk equivalent iff
•A, B are Lk1w equivalent
iff
•A º1wk B