Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Costs and Benefits of a Shared Digital Long-Term Preservation System

This paper describes the cost-benefit analysis of digital long-term preservation (LTP) that was carried out in the context of the Finnish National Digital Library Project (NDL) in 2010. The analysis was based on the assumption that as many as 200 archives, libraries, and museums will share an LTP system. The term ‘system’ shall be understood as encompassing not only information technology, but also human resources, organizational structures, policies and funding mechanisms. The cost analysis shows that an LTP system will incur, over the first 12 years, cumulative costs of €42 million, i.e. an average of €3.5 million per annum. Human resources and investments in information technology are the major cost factors. After the initial stages, the analysis predicts annual costs of circa €4 million. The analysis compared scenarios with and without a shared LTP system. The results indicate that a shared system will have remarkable benefits. At the development and implementation stages, a shared system shows an advantage of €30 million against the alternative scenario consisting of five independent LTP solutions. During the later stages, the advantage is estimated at €10 million per annum. The cumulative cost benefit over the first 12 years would amount to circa €100 million.

Monitoring Indigenous Tropical Montane Forests in the Taita Hills Using Airborne Digital Camera Imagery

The loss and degradation of forest cover is currently a globally recognised problem. The fragmentation of forests is further affecting the biodiversity and well-being of the ecosystems also in Kenya. This study focuses on two indigenous tropical montane forests in the Taita Hills in southeastern Kenya. The study is a part of the TAITA-project within the Department of Geography in the University of Helsinki. The study forests, Ngangao and Chawia, are studied by remote sensing and GIS methods. The main data includes black and white aerial photography from 1955 and true colour digital camera data from 2004. This data is used to produce aerial mosaics from the study areas. The land cover of these study areas is studied by visual interpretation, pixel-based supervised classification and object-oriented supervised classification. The change of the forest cover is studied with GIS methods using the visual interpretations from 1955 and 2004. Furthermore, the present state of the study forests is assessed with leaf area index and canopy closure parameters retrieved from hemispherical photographs as well as with additional, previously collected forest health monitoring data. The canopy parameters are also compared with textural parameters from digital aerial mosaics. This study concludes that the classification of forest areas by using true colour data is not an easy task although the digital aerial mosaics are proved to be very accurate. The best classifications are still achieved with visual interpretation methods as the accuracies of the pixel-based and object-oriented supervised classification methods are not satisfying. According to the change detection of the land cover in the study areas, the area of indigenous woodland in both forests has decreased in 1955 2004. However in Ngangao, the overall woodland area has grown mainly because of plantations of exotic species. In general, the land cover of both study areas is more fragmented in 2004 than in 1955. Although the forest area has decreased, forests seem to have a more optimistic future than before. This is due to the increasing appreciation of the forest areas.