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Please work on part 1) and part 2)! Thank you very much!! Assume we are given two countable structures (A, lessthanorequalto) and (B, lessthanorequalto), which

Please work on part 1) and part 2)! Thank you very much!!

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Assume we are given two countable structures (A, lessthanorequalto) and (B, lessthanorequalto), which both satisfy the axioms of dense linear order without endpoints (DLO + WEP). Show that you can define a type of two player back-and-forth game that shows these two structures are actually isomorphic. Be sure to explain what the players and moves are in your game. Describe two non-countable models of DLO + WEP which are not isomorphic. Here is a more or less typical set of axioms of a Boolean Algebra, a kind of structure we can investigate much like we have done with linear orders, number systems, etc. A Boolean algebra B = (B, +, middot, -, 0, 1) is a non-empty set B together with (i) A binary operation on B, denoted middot, called meet. (ii) A binary operation on B, denoted +, called join. (iii) A unary operation on B, denoted -, called complement and (iv) Two distinguished elements in B, denoted by constant symbols 0 and 1

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