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Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Asymptotic Classes, Pseudofinite Cardinality And Dimension, Alexander Van Abel
Dissertations, Theses, and Capstone Projects
We explore the consequences of various model-theoretic tameness conditions upon the behavior of pseudofinite cardinality and dimension. We show that for pseudofinite theories which are either Morley Rank 1 or uncountably categorical, pseudofinite cardinality in ultraproducts satisfying such theories is highly well-behaved. On the other hand, it has been shown that pseudofinite dimension is not necessarily well-behaved in all ultraproducts of theories which are simple or supersimple; we extend such an observation by constructing simple and supersimple theories in which pseudofinite dimension is necessarily ill-behaved in all such ultraproducts. Additionally, we have novel results connecting various forms of asymptotic classes …