THEORIES OF BALDWIN-SHI HYPERGRAPHS: THEIR ATOMIC MODELS AND REGULAR TYPES
| dc.contributor.advisor | Laskowski, Michael C | en_US |
| dc.contributor.author | Gunatilleka, Mestiyage Don Danul Kavindra | en_US |
| dc.contributor.department | Mathematics | en_US |
| dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
| dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
| dc.date.accessioned | 2019-06-21T05:34:22Z | |
| dc.date.available | 2019-06-21T05:34:22Z | |
| dc.date.issued | 2019 | en_US |
| dc.description.abstract | In [1], Baldwin and Shi studied the properties of generic structures built from certain Fraı̈ssé classes of weighted hypergraphs equipped with a notion of strong substructure. Here we focus on a particularly important class of such structures, where much stronger results are possible. We begin by fixing a finite relational language and a set of weights α. After constructing certain weighted hypergraphs with carefully chosen properties, we use these constructions to obtain an ∀∃-axiomatization for the theory of the generic, denoted by S α , and a quantifier elimination result for S α . These results, which extend those of Laskowski in [2] and Ikeda, Kikyo and Tsuboi in [3] are then used to study atomic and existentially closed models of S α , resulting in a necessary and sufficient condition on the weights that yields the existence of atomic models of thecorresponding theory. We then proceed to obtain the stability of S α and a characertization of non- forking, simplifying the proofs of some of these well known results (see [1], [4]) in the process. We identify conditions on α that guarantee that S α is non-trivial and prove that S α has the dimensional order property, a result that has only been established under certain additional hypothesis (see [5], [2]). Restricting ourselves to the case where the weights are all rational (excluding, what is essentially a single exception), we characterize the countable models up to isomorphism and show that they form an elementary chain of order type ω + 1. We also characterize the regular types of S α and explore the corresponding pregeometries. We answer a question of Pillay in [6] by providing examples of pseudofinite stable theories with non-locally modular regular types. We conclude by studying the aforementioned exception (characterized by hav- ing trivial forking) and extending some of the results to countably infinite languages. | en_US |
| dc.identifier | https://doi.org/10.13016/jrda-yda3 | |
| dc.identifier.uri | http://hdl.handle.net/1903/22103 | |
| dc.language.iso | en | en_US |
| dc.subject.pqcontrolled | Mathematics | en_US |
| dc.title | THEORIES OF BALDWIN-SHI HYPERGRAPHS: THEIR ATOMIC MODELS AND REGULAR TYPES | en_US |
| dc.type | Dissertation | en_US |
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