The Back-and-Forth Method in ω-Saturated Models
Two elements a and b in L-structures (structures whose similarity type is that of L) are said to have the same type if they satisfy the same formulas f(x) in L; the type of a is the set p a of formulas f(x) that a satisfies. What is a type but a complete theory in the language L(x) obtained by adding to L a constant symbol x? For reasons of convenience, we write this constant symbol here as a variable.
KeywordsFinite Subset Complete Theory Constant Symbol Elementary Extension Bibliographic Note
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