So far in this part we have spoken about satisfaction of sentences and methods for finding models for sets of sentences We now want to consider similar general questions concerning sets of formulas Thus instead of considering global questions, about classes of structures, we shall be considering local questions, about sets of elements, or sets of finite sequences of elements. Generally speaking, we shall be concerned with conditions on a set Δ of formulas for there to exist a structure A and an x∈ωA such thatx∈φA for all φ∈Δ.
KeywordsPrime Model Complete Theory Compactness Theorem Countable Model Infinite Subset
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