Characterizing model completeness among mutually algebraic structures
Michael C. Laskowski
TL;DR
This paper provides a characterization of when the elementary diagram of mutually algebraic structures has a model complete theory, including explicit formulas and applications to strongly minimal, trivial theories.
Contribution
It offers a new, constructive characterization of model completeness for elementary diagrams of mutually algebraic structures and applies this to strongly minimal, trivial theories.
Findings
Explicit description of existential formulas equivalent to any formula.
Characterization of model completeness in mutually algebraic structures.
Proof that elementary diagrams of models of strongly minimal, trivial theories are model complete.
Abstract
We characterize when the elementary diagram of a mutually algebraic structure has a model complete theory, and give an explicit description of a set of existential formulas to which every formula is equivalent. This characterization yields a new, more constructive proof that the elementary diagram of any model of a strongly minimal, trivial theory is model complete.
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