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Interventions
Stejskalová, Šárka ; Jezbera, Ladislav (referee) ; Gabriel, Michal (advisor)
In my bachelor's thesis I deal with the landscape and the influence of man on its changes. I focus on the landscape we visit for solitude and peace. I realize that by careful perception, a person's legacy can be found almost everywhere. In my work, I emphasizes places where nothing human happens at first glance, but on closer inspection, escape from society is almost impossible. In purely natural scenery, I find evidence of human presence in various technical buildings, telephone wires, city noise and means of transport, or in tree rowing, or sharp saw cuts and regular traces of agricultural machinery.
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Charakteristika nových hybridů silážní kukuřice
Stejskalová, Šárka
This bachelor thesis focuses on the characteristics of early maturing corn silage hybrids from the VP AGRO company. The selected hybrids were compared according to the yields of the green matter (t/ha), dry matter (t/ha and %) and according to the price level of seeds (Kč/SU). The data were collected from field trial records that took place between 2011 and 2022. These field experiments took place in the Czech potatoe agricultural sector in the Vysočina region at the following stands: Bobrová, Častrov, Horní Krupá, Okrouhlička, Počátky, Pohled, Pozovice, Radostín, Stonařov and Věž. Twelve hybrids were selected for the purpose of the study. The hybrids were subsequently divided according to the year of registration in the Czech Republic, followed by their detailed description and analysis. Based on the collected data, the following results were found. The total yields of green matter for all hybrids showed very similar and high values (50 t/ha). On the contrary the results of dry matter yields differed for each hybrid (16–18 t/ha). Additionally, similar fluctuations of dry matter in percent (34–38 %) were found. This high level of percentages of dry matter was caused by climate, soil conditions and different properties of individual hybrid. Regarding the economic comparison, the rising trend of the price level was confirmed, as is the case in the entire national sector. Seed prices have been affected by climatic, socio, political, and economic changes. One of the reasons for the price increase proved to be bad weather conditions (drought) in France, the state where the selected hybrids are bred.
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Naive set theory with exclusive interpretation of quantifiers
Blahynka, Martin ; Punčochář, Vít (advisor) ; Stejskalová, Šárka (referee)
Naive set theory can be formalised in first-order logic as a theory with one axiom (of extensionality) and one axiom schema (of unrestricted comprehension). It is widely known that this theory is inconsistent. What is less known is that a mere reinterpretation of the quantifiers in the schema of unrestricted comprehension blocks all the well-known paradoxes of naive set theory. This is the case when the quantifiers are interpreted exclusively, which is an idea that originates in Wittgenstein's Tractatus in the context of elimination of identity from logic. In the context of set theory, the idea was first used by Jaakko Hintikka thirty five years later. This thesis introduces and investigates the possibility of using exclusive interpretation of quantifiers to avoid paradoxes of naive set theory. The main criterion of success is consistency of the resulting theory. The main result of this thesis is the proof that the set theories, which use the idea of exclusive interpretation and which Hintikka left as possibly consistent, are inconsistent. The inconsistency is discussed in the context of Russell's vicious circle principle, which is found to be inadequate.
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Interventions
Stejskalová, Šárka ; Jezbera, Ladislav (referee) ; Gabriel, Michal (advisor)
In my bachelor's thesis I deal with the landscape and the influence of man on its changes. I focus on the landscape we visit for solitude and peace. I realize that by careful perception, a person's legacy can be found almost everywhere. In my work, I emphasizes places where nothing human happens at first glance, but on closer inspection, escape from society is almost impossible. In purely natural scenery, I find evidence of human presence in various technical buildings, telephone wires, city noise and means of transport, or in tree rowing, or sharp saw cuts and regular traces of agricultural machinery.
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The continuum function on singular cardinals
Stejskalová, Šárka ; Honzík, Radek (advisor) ; Verner, Jonathan (referee)
Bachelor thesis studies the behaviour of the continuum function on singular cardinals in theory ZFC. The work is divided into two parts. The focus of the first part is on the Silver's Theorem and it analyzes two different proofs of this Theorem, Silver's original proof and the second, purely combinatorial, proof by Baumgartner and Prikry. The second part is devoted to the Singular Cardinal Hypothesis, which influences the behaviour of the continuum function. In the thesis it is shown that, in the presence of large cardinals, Singular Cardinal Hypothesis is not provable in ZFC. Using Easton and Prikry forcing a model is found where the Singular Cardinal Hypothesis does not hold.
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Tree property at more cardinals
Stejskalová, Šárka ; Honzík, Radek (advisor) ; Zdomskyy, Lyubomyr (referee)
In this thesis we study the Aronszajn and special Aronszajn trees, their existence and nonexistence. We introduce the most common definition of special Aronszajn tree and some of its generalizations and we examine the relations between them. Next we study the notions of the tree property and the weak tree property at a given regular cardinal κ. The tree property means that there are no Aronszajn trees at κ and the weak tree property means that there are no special Aronszajn trees at κ. We define and compare two forcings, the Mitchell forcing and the Grigorieff forcing, and we use them to obtain a model in which the (weak) tree property holds at a given cardinal. At the end, we show how to use the Mitchell forcing to construct a model in which the (weak) tree property holds at more than one cardinal. 1
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The tree property and the continuum function
Stejskalová, Šárka ; Honzík, Radek (advisor) ; Cummings, James (referee) ; Brooke-Taylor, Andrew (referee)
The continuum function is a function which maps every infinite cardinal κ to 2κ. We say that a regular uncountable cardinal κ has the tree property if every κ-tree has a cofinal branch, or equivalently if there are no κ-Aronszajn trees. We say that a regular uncountable cardinal κ has the weak tree property if there are no special κ-Aronszajn trees. It is known that the tree property, and the weak tree property, have the following non-trivial effect on the continuum function: (∗) If the (weak) tree property holds at κ++, then 2κ ≥ κ++. In this thesis we show several results which suggest that (∗) is the only restriction which the tree property and the weak tree property put on the continuum function in addition to the usual restrictions provable in ZFC (monotonicity and the fact that the cofinality of 2κ must be greater than κ; let us denote these conditions by (∗∗)). First we show that the tree property at ℵ2n for every 1 ≤ n < ω, and the weak tree property at ℵn for 2 ≤ n < ω, does not restrict the continuum function below ℵω more than is required by (∗), i.e. every behaviour of the continuum function below ℵω which satisfies the conditions (∗) and (∗∗) is realisable in some generic extension. We use infinitely many weakly compact cardinals (for the tree property) and infinitely many Mahlo...
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The tree property and the continuum function
Stejskalová, Šárka ; Honzík, Radek (advisor) ; Cummings, James (referee) ; Brooke-Taylor, Andrew (referee)
The continuum function is a function which maps every infinite cardinal κ to 2κ. We say that a regular uncountable cardinal κ has the tree property if every κ-tree has a cofinal branch, or equivalently if there are no κ-Aronszajn trees. We say that a regular uncountable cardinal κ has the weak tree property if there are no special κ-Aronszajn trees. It is known that the tree property, and the weak tree property, have the following non-trivial effect on the continuum function: (∗) If the (weak) tree property holds at κ++, then 2κ ≥ κ++. In this thesis we show several results which suggest that (∗) is the only restriction which the tree property and the weak tree property put on the continuum function in addition to the usual restrictions provable in ZFC (monotonicity and the fact that the cofinality of 2κ must be greater than κ; let us denote these conditions by (∗∗)). First we show that the tree property at ℵ2n for every 1 ≤ n < ω, and the weak tree property at ℵn for 2 ≤ n < ω, does not restrict the continuum function below ℵω more than is required by (∗), i.e. every behaviour of the continuum function below ℵω which satisfies the conditions (∗) and (∗∗) is realisable in some generic extension. We use infinitely many weakly compact cardinals (for the tree property) and infinitely many Mahlo...
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Tree property at more cardinals
Stejskalová, Šárka ; Honzík, Radek (advisor) ; Zdomskyy, Lyubomyr (referee)
In this thesis we study the Aronszajn and special Aronszajn trees, their existence and nonexistence. We introduce the most common definition of special Aronszajn tree and some of its generalizations and we examine the relations between them. Next we study the notions of the tree property and the weak tree property at a given regular cardinal κ. The tree property means that there are no Aronszajn trees at κ and the weak tree property means that there are no special Aronszajn trees at κ. We define and compare two forcings, the Mitchell forcing and the Grigorieff forcing, and we use them to obtain a model in which the (weak) tree property holds at a given cardinal. At the end, we show how to use the Mitchell forcing to construct a model in which the (weak) tree property holds at more than one cardinal. 1
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