Undergraduate Honors Thesis
Model-Theoretic Limits and the Hrushovski Construction Public Deposited
- Abstract
Roland Fraı̈ssé provided a model-theoretic framework for constructing a homogeneous model from a countable class of structures through amalgamation. This process was then expanded upon by Hrushovski, who modified the construction to operate under weaker conditions. These approaches allowed the creation of strongly minimal models with pathological geometries in order to disprove conjectures that aimed to classify strongly minimal models, including Zil’ber’s Conjecture. It is the aim of this paper to present an introduction into model theory and model-theoretic nature of limits, including the Fraı̈ssé and Hrushovski constructions. This will be in the context of understanding methods for the creation of homogeneous structures, and understanding where these limit structures have appeared in mathematics.
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- Date Awarded
- 2022-04-05
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- Last Modified
- 2022-04-12
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Thesis_Final.pdf | 2022-04-12 | Public | Download |