Formulas and properties

2021/04/01 by Sudoplatov, Sergey V.
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2104.00468

Abstract

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties are described. Characteristics for generic sentences and generic theories with respect to properties are described and characterized.

Related

• Definable families of theories, related calculi and ranks
• Expansions and restrictions of structures and theories, their hierarchies
• Ranks for families of all theories of given languages
• Arities and aritizabilities of first-order theories
• Algebraic closures and their variations