On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

The Mediated Immediacy : João Batista Libanio and the Question of Latin American Liberation Theology

This study is a systematic analysis of mediated immediacy in the production of the Brazilian professor of theology João Batista Libanio. He stresses both ethical mediation and the immediate character of the faith. Libanio has sought an answer to the problem of science and faith. He makes use of the neo-scholastic distinction between matter and form. According to St. Thomas Aquinas, God cannot be known as a scientific object, but it is possible to predicate a formal theological content of other subject matter with the help of revelation. This viewpoint was emphasized in neo-Thomism and supported by the liberation theologians. For them, the material starting point was social science. It becomes a theologizable or revealable (revelabile) reality. This social science has its roots in Latin American Marxism which was influenced by the school of Louis Althusser and considered Marxism a science of history . The synthesis of Thomism and Marxism is a challenge Libanio faced, especially in his Teologia da libertação from 1987. He emphasized the need for a genuinely spiritual and ethical discernment, and was particularly critical of the ethical implications of class struggle. Libanio s thinking has a strong hermeneutic flavor. It is more important to understand than to explain. He does not deny the need for social scientific data, but that they cannot be the exclusive starting point of theology. There are different readings of the world, both scientific and theological. A holistic understanding of the nature of religious experience is needed. Libanio follows the interpretation given by H. C. de Lima Vaz, according to whom the Hegelian dialectic is a rational circulation between the totality and its parts. He also recalls Oscar Cullmann s idea of God s Kingdom that is already and not yet . In other words, there is a continuous mediation of grace into the natural world. This dialectic is reflected in ethics. Faith must be verified in good works. Libanio uses the Thomist fides caritate formata principle and the modern orthopraxis thinking represented by Edward Schillebeeckx. One needs both the ortho of good faith and the praxis of the right action. The mediation of praxis is the mediation of human and divine love. Libanio s theology has strong roots in the Jesuit spirituality that places the emphasis on contemplation in action.

Distribution of non-biting midges (Diptera, Chironomidae) in subarctic lakes of Finnish Lapland applications in lake classification and palaeolimnology

Climate change contributes directly or indirectly to changes in species distributions, and there is very high confidence that recent climate warming is already affecting ecosystems. The Arctic has already experienced the greatest regional warming in recent decades, and the trend is continuing. However, studies on the northern ecosystems are scarce compared to more southerly regions. Better understanding of the past and present environmental change is needed to be able to forecast the future. Multivariate methods were used to explore the distributional patterns of chironomids in 50 shallow (≤ 10m) lakes in relation to 24 variables determined in northern Fennoscandia at the ecotonal area from the boreal forest in the south to the orohemiarctic zone in the north. Highest taxon richness was noted at middle elevations around 400 m a.s.l. Significantly lower values were observed from cold lakes situated in the tundra zone. Lake water alkalinity had the strongest positive correlation with the taxon richness. Many taxa had preference for lakes either on tundra area or forested area. The variation in the chironomid abundance data was best correlated with sediment organic content (LOI), lake water total organic carbon content, pH and air temperature, with LOI being the strongest variable. Three major lake groups were separated on the basis of their chironomid assemblages: (i) small and shallow organic-rich lakes, (ii) large and base-rich lakes, and (iii) cold and clear oligotrophic tundra lakes. Environmental variables best discriminating the lake groups were LOI, taxon richness, and Mg. When repeated, this kind of an approach could be useful and efficient in monitoring the effects of global change on species ranges. Many species of fast spreading insects, including chironomids, show a remarkable ability to track environmental changes. Based on this ability, past environmental conditions have been reconstructed using their chitinous remains in the lake sediment profiles. In order to study the Holocene environmental history of subarctic aquatic systems, and quantitatively reconstruct the past temperatures at or near the treeline, long sediment cores covering the last 10000 years (the Holocene) were collected from three lakes. Lower temperature values than expected based on the presence of pine in the catchment during the mid-Holocene were reconstructed from a lake with great water volume and depth. The lake provided thermal refuge for profundal, cold adapted taxa during the warm period. In a shallow lake, the decrease in the reconstructed temperatures during the late Holocene may reflect the indirect response of the midges to climate change through, e.g., pH change. The results from three lakes indicated that the response of chironomids to climate have been more or less indirect. However, concurrent shifts in assemblages of chironomids and vegetation in two lakes during the Holocene time period indicated that the midges together with the terrestrial vegetation had responded to the same ultimate cause, which most likely was the Holocene climate change. This was also supported by the similarity in the long-term trends in faunal succession for the chironomid assemblages in several lakes in the area. In northern Finnish Lapland the distribution of chironomids were significantly correlated with physical and limnological factors that are most likely to change as a result of future climate change. The indirect and individualistic response of aquatic systems, as reconstructed using the chironomid assemblages, to the climate change in the past suggests that in the future, the lake ecosystems in the north do not respond in one predictable way to the global climate change. Lakes in the north may respond to global climate change in various ways that are dependent on the initial characters of the catchment area and the lake.