3 resultados para isomorphism

em Helda - Digital Repository of University of Helsinki


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Integrating biodiversity conservation into forest management in non-industrial private forests requires changes in the practices of those public and private actors that have implementing responsibilities and whose strategic and operational opportunities are at stake. Understanding this kind of context-dependent institutional adaptation requires bridging between two analytical approaches: policy implementation and organizational adaptation, backed up with empirical analysis. The empirical analyses recapitulated in this thesis summary address organizational competences, specialization, professional judgment, and organizational networks. The analyses utilize qualitative and quantitative data from public and private sector organizations as well as associations. The empirical analyses produced stronger signals of policy implementation than of organizational adaptation. The organizations recognized the policy and social demand for integrating biodiversity conservation into forest management and their professionals were in favor of conserving biodiversity. However, conservation was integrated to forest management so tightly that it could be said to be subsumed by mainstream forestry. The organizations had developed some competences for conservation but the competences did not differentiate among the organizations other than illustrating the functional differences between industry, administration and associations. The networks that organizations depended on consisted of traditional forestry actors and peers both in planning policy and at the operational level. The results show that he demand for biodiversity conservation has triggered incremental changes in organizations. They can be considered inert regarding this challenge. Isomorphism is advanced by hierarchical guidance and standardization, and by professional norms. Analytically, this thesis contributes to the understanding of organizational behavior across the public and private sector boundaries. The combination of a policy implementation approach inherent in analysis of public policies in hierarchical administration settings, and organizational adaptation typically applied to private sector organizations, highlights the importance of institutional interpretation. Institutional interpretation serves the understanding of the empirically identified diversions from the basic tenets of the two approaches. Attention to institutions allows identification of the overlap of the traditionally segregated approaches.

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In this paper we define a game which is played between two players I and II on two mathematical structures A and B. The players choose elements from both structures in moves, and at the end of the game the player II wins if the chosen structures are isomorphic. Thus the difference of this to the ordinary Ehrenfeucht-Fra¨ıss´e game is that the isomorphism can be arbitrary, whereas in the ordinary EF-game it is determined by the moves of the players. We investigate determinacy of the weak EF-game for different (the length of the game) and its relation to the ordinary EF-game.

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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