Let σpo := (<) be the usual signature for strict partial orders. A linear order (A, <) is called dense if for any a, b ∈ A with a < b, there is c ∈ A such that a < c < b. a. Let σpo∞ := (<, { cn : n ∈ ℕ) and add axioms to DLO to get a theory DLO∞ axiomatizing the class of dense linear orders without endpoints that satisfy ci < ci+1 for all i ∈ ℕ. b. Provide three nonisomorphic countable models of DLO∞. Remark: In fact, DLO∞ has exactly three non-isomorphic countable models, but you do not need to prove this.
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Let σpo := (<) be the usual signature for strict partial orders. A linear order (A, <) is called dense if for any a, b ∈ A with a < b, there is c ∈ A such that a < c < b.
a. Let σpo∞ := (<, { cn : n ∈ ℕ) and add axioms to DLO to get a theory DLO∞ axiomatizing the class of dense linear orders without endpoints that satisfy ci < ci+1 for all i ∈ ℕ.
b. Provide three nonisomorphic countable models of DLO∞. Remark: In fact, DLO∞ has exactly three non-isomorphic countable models, but you do not need to prove this.
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