The Borel Complexity of Isomorphism for Some First Order Theories

In this work we consider several instances of the following problem: "how complicated can the isomorphism relation for countable models be?"' Using the Borel reducibility framework, we investigate this question with regard to the space of countable models of particular complete first-order theories. We also investigate to what extent this complexity is mirrored in the number of back-and-forth inequivalent models of the theory. We consider this question for two large and related classes of theories. First, we consider o-minimal theories, showing that if T is o-minimal, then the isomorphism relation is either Borel complete or Borel. Further, if it is Borel, we characterize exactly which values can occur, and when they occur. In all cases Borel completeness implies lambda-Borel completeness for all lambda. Second, we consider colored linear orders, which are (complete theories of) a linear order expanded by countably many unary predicates. We discover the same characterization as with o-minimal theories, taking the same values, with the exception that all finite values are possible except two. We characterize exactly when each possibility occurs, which is similar to the o-minimal case. Additionally, we extend Schirrman's theorem, showing that if the language is finite, then T is countably categorical or Borel complete. As before, in all cases Borel completeness implies lambda-Borel completeness for all lambda.

Integrating Environmental Justice and Social-Ecological Resilience for Successful Adaptation to Climate Change: Lessons from African American Communities on the Eastern Shore of the Chesapeake Bay

This research concerns the conceptual and empirical relationship between environmental justice and social-ecological resilience as it relates to climate change vulnerability and adaptation. Two primary questions guided this work. First, what is the level of resilience and adaptive capacity for social-ecological systems that are characterized by environmental injustice in the face of climate change? And second, what is the role of an environmental justice approach in developing adaptation policies that will promote social-ecological resilience? These questions were investigated in three African American communities that are particularly vulnerable to flooding from sea-level rise on the Eastern Shore of the Chesapeake Bay. Using qualitative and quantitative methods, I found that in all three communities, religious faith and the church, rootedness in the landscape, and race relations were highly salient to community experience. The degree to which these common aspects of the communities have imparted adaptive capacity has changed over time. Importantly, a given social-ecological factor does not have the same effect on vulnerability in all communities; however, in all communities political isolation decreases adaptive capacity and increases vulnerability. This political isolation is at least partly due to procedural injustice, which occurs for a number of interrelated reasons. This research further revealed that while all stakeholders (policymakers, environmentalists, and African American community members) generally agree that justice needs to be increased on the Eastern Shore, stakeholder groups disagree about what a justice approach to adaptation would look like. When brought together at a workshop, however, these stakeholders were able to identify numerous challenges and opportunities for increasing justice. Resilience was assessed by the presence of four resilience factors: living with uncertainty, nurturing diversity, combining different types of knowledge, and creating opportunities for self-organization. Overall, these communities seem to have low resilience; however, there is potential for resilience to increase. Finally, I argue that the use of resilience theory for environmental justice communities is limited by the great breadth and depth of knowledge required to evaluate the state of the social-ecological system, the complexities of simultaneously promoting resilience at both the regional and local scale, and the lack of attention to issues of justice.