La coordination et les phrases juxtaposées en français

Coordination and juxtaposed sentences The object of this study is the examination of the relations between juxtaposed clauses in contemporary French. The matter in question is sentences which are composed of several clauses adjoined without a conjunction or other connector, as in: Je détournai les yeux, mon c ur se mit à battre. The aim of the study is to determine, which quality is the relation in these sentences and, on the other hand, what is the part of the coordination there. Furthermore, what is this relation of coordination, which, according to some grammars, manifests through a conjunction of coordination, but which, according to some others is marked in juxtaposed sentences through different features. The study is based on a corpus of written French from literary and journalistic text sources. Syntactic, semantic and textual properties in the clauses are discussed. The analysis points to differences so, it has been noted, in each case, if one of the clauses is affirmative and the other negative and if in the second clause, the subject has not been repeated. Also, an analysis has been made on the ground of the tense, mode, phrase structure type, and thematic structure, taking into account, in each case, if the clauses are identical or different. Punctuation has been one of the properties considered. The final aim has been to eliminate gradually, based on the partition of properties, subordinate sentences, so that only the hard core of coordinate sentences remains. In this way, the coordination could be defined similarly as the phoneme is defined as a group of distinctive features. The quantitative analyses have led to the conclusion that the sentences which, from a semantic point of view, are interpreted as coordinating, contain the least of these differences, while the sentences which can be considered as subordinating present the most of these differences. The conditions of coordination are, in that sense, hierarchical, so that the syntactic constraints have to make room for semantic, textual and cognitive factors. It is interesting to notice that everyone has the ability to produce correct coordinating structures and recognize incorrect coordinating structures. This can be explained by the human ability to categorize which has been widely researched in the semantic of prototype. The study suggests that coordination and subordination could be considered as prototypical cognitive categories based on different linguistic and pragmatic features.

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.

Weak Ehrenfeucht-Fraïssé Games

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.

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