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Generellt sätt misslyckas människor ofta att göra korrekta bedömningar baserade på principerna för sannolikhetsteori, vilket kan leda till det så kallade konjunktionsfelet. Konjunktionsfelet innebär att två kombinerade subkategorier anses mer troligt än en huvudkategori. “Nested-set”-hypotesen föreslår att konjunktionsfelet kan motverkas genom att ta hänsyn till relationen mellan kategorier och subkategorier. Denna uppsats ämnar undersöka om konjunktionsfelet minskar med ökad insikt om “nested-set”-strukturen med hjälp av få ledtrådar. Sextio deltagare fördelades randomiserat i två grupper med olika mycket ledtrådar om “nested-set”-strukturen. Resultaten indikerar att två ledtrådar om “nested-set”-strukturen är tillräcklig med information för att göra signifikant fler korrekta sannolikhetsbedömningar. En ledtråd var inte tillräcklig.  Konklusionen är att vi med hjälp av tillräckligt många ledtrådar kan förstå relationen mellan kategori- och subkategori och således fatta korrekta beslut utifrån sannolikhetslära. / Generally, people often fail to make accurate judgments according to the principles of probability theory which can lead to the so called conjunction fallacy. The conjunction fallacy consists of assigning a higher probability to two combined subcategories than one main category. The “nested-set” hypothesis proposes that the conjunction fallacy can be countered by accounting for the relationship between categories and subcategories. This thesis aims to investigate if the conjunction fallacy is reduced by giving participants few clues that reveal the set structure. Sixty participants were randomly divided into two groups with different clues about the “nested-set” structure. The results indicated that two clues about the nested set structure were enough information to make significantly more accurate probability estimates. One clue was not enough. Our conclusion is that with enough clues we are able to understand the relation between category and sub category and thus make correct decisions based on probability theory.

The purpose of this paper is to explore some of the properties of the Cantor set and to extend the idea of this set to metric spaces, in general, and to other sets of real numbers and sets in N-dimensional Euclidean space, in particular.

Assume AD+V=L(R). In the first chapter, let W^1_1 denote the club measure on \omega_1. We analyze the embedding j_{W^1_1}\restr HOD from the point of view of inner model theory. We use our analysis to answer a question of Jackson-Ketchersid about codes for ordinals less than \omega_\omega. In the second chapter, we provide an indiscernibles analysis for models of the form L[T_n,x]. We use our analysis to provide new proofs of the strong partition property on \delta^1_{2n+1}

We present the results from three papers concerning partitions of vector spaces V over the set R of reals and of the set of lines in V.

The first theme which I focus on, is the life and work of the violin maker Václav Lanc. I explain his theories and methods of the violin building and setting up. I also approximate the luthiers craft and details of the string instruments construction. Then I write about the development of violin making in the Czech republic and also in the World and I emphasize the historical consequences. Finally I deal with the string musical instruments which are used at the basic music schools. The purpose is to minimize the problems, which teachers and pupils have with the daily maintenance and with setting up of the violin. At the end, for the youngest pupils, I dedicate the "Ten commandments" - How they should to look after their musical instruments. Keywords The building, the set up, the defects.

This thesis concerns two-point sets, which are subsets of the real plane which intersect every line in exactly two points. The existence of two-point sets was first shown in 1914 by Mazukiewicz, and since this time, the properties of these objects have been of great intrigue to mathematicians working in both topology and set theory. Arguably, the most famous problem about two-point sets is concerned with their so-called "descriptive complexity"; it remains open, and it appears to be deep. An informal interpretation of the problem, which traces back at least to Erdos, is: The term "two-point" set can be defined in a way that it is easily understood by someone with only a limited amount of mathemat- ical training. Even so, how hard is it to construct a two-point set? Can one give an effective algorithm which describes precisely how to do so? More formally, Erdos wanted to know if there exists a two-point set which is a Borel subset of the plane. An essential tool in showing the existence of a two-point set is the Axiom of Choice, an axiom which is taken to be one of the basic truths of mathematics.

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