Chapter Four

The Löwenheim Normal Form

4.1 THE LÖWENHEIM NORMAL FORM OF AN EQUATION

4.1.1 As I stated at the beginning of the previous chapter, the first part of Löwenheim's proof consists in showing that every equation is equivalent to an equation that has a certain normal form. Löwenheim considers an equation to be in normal form if it has the form -179547685, where F is a quantifierfree formula, -179547485 represents a possibly empty string of existential quantifiers (either type Σ or ) and II represents a possibly empty string of universal quantifiers (as a special ...

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