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Simple QE for Dense Linear Orders
Example of dense linear order: rational numbers with less-than relation. (It works in the same way for real numbers with less-than relation.)
Theory of Dense Linear Orders
Language . Atomic formulas are of two forms:
Literals are either atomic formulas or their negations.
Formulas are the formulas that are closed formulas that are true in the structure
or rational numbers.
Normal form of Formulas
We have seen that it suffices to eliminate quantifiers from conjunctions of literals.
Can we assume that literals are of a special form?
Example: simplify these formulas:
If we have three concrete values for , what is the form of the strongest type of a formula that we could write about them in this language? (atomic type formula)