Die Alternativensemantik nach (Rooth, 1985, 1992) geht davon aus, dass sprachlicher Fokus eine Menge von Alternativen evoziert und Fokuspartikeln auf diese Menge Bezug nehmen. Die vorliegende Dissertation untersucht den Ein uss von Fokuspartikeln und prosodischem Fokus auf die mentale Repräsentation von Alternativenmengen. Im Speziellen wurden die sprachlichen und kognitiven Mechanismen, die am Aufbau einer Alternativenmenge beteiligt sind, mittels psycholinguistischer Experimente getestet. Experiment 1a und 1b untersuchen späte Repräsentation der gesamten Alternativenmenge. Die Experimente zeigen, dass Fokuspartikeln zu einer reicheren Enkodierung der Alternativenmenge führen, was sich in einem verbesserten Gedächtnisabruf äußert. Experiment 2 und 3 untersuchen die Prozesse, die am Aufbau von Alternativenmengen beteiligt sind. In Experiment 2 (Probe Recognition) führten Fokuspartikeln zu Interferenzeffekten beim Erkennen von erwähnten Alternativen sowie bei der Ablehnung nicht-erwähnter Alternativen. Eine weitere Analyse und Experiment 4 untersuchen die Mitglieder der Alternativenmenge. Die Daten deuten darauf hin, dass die Alternativenmenge aus sämtlichen möglichen Ersetzungen des fokussierten Elements inklusive unrelatierter Elemente besteht. Im Vergleich von intonatorischem Fokus und Fokuspartikeln (Experiment 5 und 6) zeigte sich, dass Fokus den Abruf von kontextuellen Alternativen erleichtert während Fokuspartikeln zu zusätzlichen Kompetitionseffekten führen. Im Allgemeinen liefert deutet die vorliegende Dissertation darauf hin, dass intonatorischer Fokus eine Alternativenmenge im Kopf des Hrers evoziert und dabei hilft relevante Alternativen zu identifizieren. Fokuspartikeln haben eine zusätzliche Funktion und führen whrend der Sprachverarbeitung zu einem strkeren Wettberwerb zwischen Mitgliedern der Alternativenmenge. / According to Rooth'' alternative semantics (Rooth, 1985, 1992), focus evokes a set of alternatives and that focus particles make reference to this set. The present thesis examines the impact of focus particles and intonational focus on the mental representation of alternatives. In particular, it explores the linguistic and cognitive mechanisms that underlie the establishment of alternative sets in a series of psycholinguistic experiments. Two delayed recall experiments (Exp. 1a and 1b) revealed that participants were better at recalling mentioned alternatives to a focused element when the discourse contained the particles only or even. Experiments 2 and 3 found interference effects of focus particles in the recognition of mentioned alternatives and the rejection of unmentioned alternatives. An additional analysis and Experiment 4 indicate that the set of alternatives consists of various possible replacements of the focused element. Experiment 5 showed that contrastive accents facilitated the retrieval of alternatives while focus particles caused interference effects relative to the condition with an L+H* accent. Overall, this thesis indicates that intonational focus activates alternatives in the listeners mind and helps identifying relevant alternatives. Focus particles, on the other hand, cause stronger competition between the focused element and its alternatives.

The theory presented here stemmed from years of teaching analysis at pre-university level first using the concept of infinitesimal as defined in nonstandard analysis by Robinson, then the concept of ultrasmall as defined in our joint work with Hrbacek and Lessmann presented in the appendix. This research led to the question : If one has finite yet ultralarge quantities, is it possible to avoid infinite quantities ? The alternative set theory of Vopěnka is a theory of finite sets including classes that can be infinite. The theory of objects is a merger of certain axioms of Vopěnka with axioms that determine levels of visibility as in relative analysis. We took as first principle : $x\subseteq y\Rightarrow x\sqsubseteq y$, which specifies that if object $x$ is included in object $y$, then $x$ "appears" at the level of $y$. This statement would be false with infinite quantities and is in fact a characterisation of finite sets : this is a well-known theorem of nonstandard analysis. The introduction of this principle as starting point is making a strong point that all objects will be finite - in the usual sense of the word. The other founding axiom is Gordon and Andreev's axiom schema : If $\Phi$ is a formula, and if $\Phi(\emptyset)$ is true and that $\Phi(x)$ and $\Phi(y)$ imply $\Phi(x\cup\{y\})$, then $\Phi(x)$ is true for all $x$. An emphasis is made on the concept of contextual formulae. This concept is one of our contributions to relative analysis of Hrbacek and determines an equivalence to well-formed formulae. We show that the resulting system is relatively consistent with Hrbacek's FRIST and Péraire's RIST which are conservative extensions of ZFC. The theory of objects extends set theory of Zermelo and Fraenkel without choice and with negation of the infinity axiom. Integers and rationals are defined and endowed with an ultraproximity relation. A draft of a construction of "numeric grains" is presented : these numbers could prove to have properties sufficiently similar to real numbers to allow to perform analysis.

La théorie présentée ici est issue d'années d'enseignement de l'analyse au niveau pré-universitaire en utilisant d'abord le concept d'infiniment petit, tel que défini dans l'analyse nonstandard de Robinson, puis ensuite d'ultrapetit, tel que défini dans notre travail en collaboration avec Hrbacek et Lessmann et présenté en annexe. A la suite de ces recherches, s'est posée la question : Si l'on a à disposition des quantités finies mais ultragrandes, est-il possible de se passer de quantités dites infinies ? La théorie alternative des ensembles de Vopěnka est une théorie avec des ensembles finis et des classes qui, elles, peuvent être infinies. La théorie des objets est le résultat d'un mélange de certains axiomes de Vopěnka avec des axiomes déterminant des niveaux de visibilité tels que dans l'analyse relative. On s'est donné comme premier principe : $x\subseteq y\Rightarrow x\sqsubseteq y$ qui spécifie que si l'objet $x$ est inclus dans l'objet $y$, alors $x$ "paraît" au niveau de $y$. Cette affirmation serait fausse avec des quantités infinies ; elle est néanmoins une caractérisation des ensembles finis : cela est bien connu en analyse nonstandard. L'introduction de ce principe comme point de départ est donc une affirmation forte que les objets devront être finis au sens habituel de ce terme. L'autre axiome fondateur ici est le schéma d'axiomes d'induction de Gordon et Andreev : Si $\Phi$ est une formule, et si $\Phi(\emptyset)$ est vrai et que $\Phi(x)$ et $\Phi(y)$ impliquent $\Phi(x\cup\{y\})$, alors $\Phi(x)$ est vrai pour tout $x$. Un accent particulier est mis sur le concept de formules dites contextuelles. Ce concept est une de nos contributions à l'analyse relative de Hrbacek et détermine les formules bien formées. On montre que le système qui en résulte est relativement cohérent avec la théorie FRIST de Hrbacek et la théorie RIST de Péraire qui sont elles-mêmes des extensions conservatives de ZFC. La théorie des objets est une extension de la théorie des ensembles de Zermelo et Fraenkel sans axiome du choix et négation de l'axiome de l'infini. Les nombres entiers et rationnels sont définis et ces derniers sont munis de relations d'ultraproximité. Une ébauche d'une construction de "grains numériques" est présentée : ces nombres pourraient avoir des propriétés suffisamment semblables aux nombres réels pour permettre de faire de l'analyse. / The theory presented here stemmed from years of teaching analysis at pre-university level first using the concept of infinitesimal as defined in nonstandard analysis by Robinson, then the concept of ultrasmall as defined in our joint work with Hrbacek and Lessmann presented in the appendix. This research led to the question : If one has finite yet ultralarge quantities, is it possible to avoid infinite quantities ? The alternative set theory of Vopěnka is a theory of finite sets including classes that can be infinite. The theory of objects is a merger of certain axioms of Vopěnka with axioms that determine levels of visibility as in relative analysis. We took as first principle : $x\subseteq y\Rightarrow x\sqsubseteq y$, which specifies that if object $x$ is included in object $y$, then $x$ "appears" at the level of $y$. This statement would be false with infinite quantities and is in fact a characterisation of finite sets : this is a well-known theorem of nonstandard analysis. The introduction of this principle as starting point is making a strong point that all objects will be finite - in the usual sense of the word. The other founding axiom is Gordon and Andreev's axiom schema : If $\Phi$ is a formula, and if $\Phi(\emptyset)$ is true and that $\Phi(x)$ and $\Phi(y)$ imply $\Phi(x\cup\{y\})$, then $\Phi(x)$ is true for all $x$. An emphasis is made on the concept of contextual formulae. This concept is one of our contributions to relative analysis of Hrbacek and determines an equivalence to well-formed formulae. We show that the resulting system is relatively consistent with Hrbacek's FRIST and Péraire's RIST which are conservative extensions of ZFC. The theory of objects extends set theory of Zermelo and Fraenkel without choice and with negation of the infinity axiom. Integers and rationals are defined and endowed with an ultraproximity relation. A draft of a construction of "numeric grains" is presented : these numbers could prove to have properties sufficiently similar to real numbers to allow to perform analysis.

The thesis follows on Petr Vopìnka's alternative theory of sets and semisets by extending notions of in nite closeness and monad for real spaces of several variables. It speci es and explains on examples the basic terminology of this theory, namely notions of sets, semisets and domains. It brings up two worlds | an ancient and a classical one | by which it shows a dual way of looking at real functions of several variables. That is used for examining local properties like continuity, limit or derivative of a function at a point. The peak of the thesis is an alternative formulation of the implicit function theorem and the inverse function theorem. The thesis also contains translation rules, which allow us to reformulate all these results from an alternative into a traditional formulation used in mathematical analysis.