peter mcburney qslwqxrfliverpoolacuk dear lotfi within model theory aka metamathematics mathematics mathematical structures considerable literature devoted determining whether two mathematical structures various precise definitions literature constitutes mathematical theory equivalence believe abstract theory similarity would need generalize one common method used make determination equivalence structures form imagined multiparty game two players different objectives ehrenfeuchtfraisse games example one player tries demonstrate nonequivalence two structures player tries counter demonstration introductory books model theory usually include discussion games eg see chapter 3 doets chapter 3 hodges details peter mcburney university liverpool uk bookdoetsbook96 author kees doets title basic model theory publisher european association logic language information folli year 1996 series studies logic language information address center study language information stanford ca usa bookhodgesbook97 author wilfrid hodges title shorter model theory publisher cambridge university press year 1997 address cambridge uk fri 08 aug 2008 092316 0000 uai define similarity