Zariski structures and simple theories - DSpace@MIT
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This MIT thesis pushes the boundaries of geometric stability theory by asking whether the rich structure of algebraic geometry can be transplanted into the wilder, more chaotic world of simple theories.
Geometric Stability TheoryZariski StructuresSimple TheoriesModel Theory
Theory Briefing
- The thesis generalises Zariski structures — geometric frameworks from algebraic geometry — to apply to simple theories beyond stable ones.
- Lascar Strong Types serve as the minimal building blocks, letting the author probe how much geometric order survives in simple, less-tame logical settings.
- The work tests whether stability theory's powerful classification tools can stretch into simple theories, which famously resist full geometric domestication.