In the first part of the paper, we show that if ω ≤ κ < λ are cardinals, κ <κ = κ, and λ is weakly compact, then in V [M(κ, λ)] the tree property at λ = κ ++V [M(κ,λ)] is indestructible under all κ + -cc forcing notions which live in V [Add(κ, λ)], where Add(κ, λ) is the Cohen forcing for adding λ-many subsets of κ and M(κ, λ) is the standard Mitchell forcing for obtaining the tree property at λ. This result has direct applications to Prikry-type forcing notions and generalized cardinal invariants. In the second part, we assume that λ is supercompact and generalize the construction and obtain a model V * , a generic extension of V , in which the tree property at (κ ++ ) V * is indestructible under all κ + -cc forcing notions living in V [Add(κ, λ)], and in addition by all forcing notions living in V * which are κ + -closed and "liftable" in a prescribed sense (such as κ ++ -directed closed forcings or well-met forcings which are κ ++ -closed with the greatest lower bounds).

In this paper we use Grigorieff forcing to obtain the tree property at the second successor of a regular uncountable cardinal κ. We also show that Silver forcing can be used to obtain the tree property at ℵ 2. Keywords: Grigorieff forcing, Silver forcing, tree property AMS subject code classification: 03E05 1 Jensen [Jen72] proved that the existence of a special μ +-Aronszajn tree is equivalent to the existence of a combinatorial object called the weak square (* μ). * μ is strictly weaker than the assumption κ <κ = κ.

This study examines aluminium as a potentially phytotoxic element in acidic forest soils. Concentrations of Al forms in soils are generally controlled by soil chemical conditions, such as pH, organic matter, base cation contents, etc. Moreover, soil conditions are influenced by the vegetation cover. This study analyzed the distribution of Al forms in soils after changes in vegetation. HPLC/IC was used for the separation of three Al fractions in two soil extracts according to their charge. An aqueous extract (AlH2O) simulated the natural soil conditions and bioavailable Al fractions. Potentially available Al form was represented by a 0.5 M KCl extract (AlKCl). We demonstrated that the vegetation type influences the concentrations of different Al fractions, mainly in the surface organic horizons. Differences were more common in the KCl extract. The trivalent fraction was less influenced by vegetation changes than the monoand divalent fractions. Afforestation increased the concentrations of AlKCl and AlH2O. In contrast, grass expansion after deforestation led to significantly decreased concentrations of AlKCl and AlH2O. Concentrations of AlH2O in organic horizons were higher in spruce forest than in beech forest. A long-term effect of liming on soil pH and concentrations of potentially toxic Al fractions was not apparent. The results provide information on the variations of Al fractions distributions following vegetation type changes and indicate the existence of some natural mechanisms controlling Al toxicity. Furthermore, the results can be used in the management of forested areas endangered by soil acidification.

Identification of Andosols is primarily based upon the content of their colloidal constituentsclay and metal-humus complexes-and on the determining of andic properties. This needs time and costconsuming geochemical analyses. Our primary aim of this study is to describe the magnetic and geochemical properties of soils rich in iron oxides derived from strongly magnetic volcanic basement (in this case Andosols). Secondary aim is to explore links between magnetic and chemical parameters of andic soils with respect to genesis factors: parent material age, precipitation, and thickness of the soil profile. Six pedons of andic properties, developed on basaltic lavas, were analyzed down to parent rock by a set of magnetic and geochemical methods. Magnetic data of soil and rock samples reflect the type, concentration, and particlesize distribution of ferrimagnetic minerals. Geochemical data include soil reaction (pH in H 2 O), cation exchange capacity, organic carbon, and different forms of extractable iron and aluminum content. Our results suggest the following: (1) magnetic measurements of low-field mass-specific magnetic susceptibility can be a reliable indicator for estimating andic properties, and in combination with thermomagnetic curves may be suitable for discriminating between alu-andic and sil-andic subtypes. (2) In the studied Andosols, strong relationships were found between (a) magnetic grain-size parameters, precipitation, and exchangeable bases; (b) concentration of ferrimagnetic particles and degree of crystallization of free iron; and (c) parameters reflecting changes in magneto-mineralogy and soil genesis (parent material age 1 soil depth).

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