We show that if κ is a weakly compact cardinal, then $\left( \matrix \kappa ^{+} \\ \kappa\endmatrix \right)\rightarrow \left(\left( \matrix \alpha \\ \kappa \endmatrix \right)_{m}\left( (...) \matrix \kappa ^{n} \\ \kappa \endmatrix \right)_{\mu}\right)^{1,1}$ for any ordinals α < κ⁺ and µ < κ, and any finite ordinals m and n. This polarized partition relation represents the statement that for any partition $\kappa \times \kappa ^{+}=\underset i<m\to{\bigcup }K_{i}\cup \underset j<\mu \to{\bigcup }L_{j}$ of κ × κ⁺ into m + µ pieces either there are A ∈ [κ]κ, B ∈ [κ⁺]α, and i < m with A × B ⊆ Ki or there are C ∈ [κ]κ, D ∈ [κ⁺]α, and j < μ with C × D ⊆ Lj. Related results for measurable and almost measurable κ are also investigated. Our proofs of these relations involve the use of elementary substructures of set models of large fragments of ZFC. (shrink)
There is a constructive method to define a structure of simple k -cyclic Post algebra of order p , L p , k , on a given finite field (...) F ( p k ), and conversely. There exists an interpretation Φ 1 of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L p , k into the variety $${\mathcal{V}(F(p^k))}$$ generated by F ( p k ) and an interpretation Φ 2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that Φ 2 Φ 1 ( B ) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and Φ 1 Φ 2 ( R ) = R for every $${R \in \mathcal{V}(F(p^k))}$$. In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)
This article presents an overview ofregulations, guidelines and societal debates ineight member states of the EC about a)embryonic and fetal tissue transplantation(EFTT), and b) the use (...) class='Hi'> of human embryonic stemcells (hES cells) for research into celltherapy, including `therapeutic' cloning. Thereappears to be a broad acceptance of EFTT inthese countries. In most countries guidance hasbeen developed. There is a `strong' consensusabout some of the central conditions for `goodclinical practice' regarding EFTT.International differences concern, amongstothers, some of the informed consent issuesinvolved, and the questions whether anintermediary organisation is necessary, whetherthe methods of abortion may be influenced bythe possible use of EFT, and whether EFTTshould only be used for the experimentaltreatment of rare disorders. The potential useof hES cells for research into cell therapy hasgiven a new impetus to the debate about (human)embryo research. The therapeutic prospects withregard to the retrieval and research use of hEScells appear to function as a catalyst for theintroduction of less restrictive regulationsconcerning research with spare embryos, atleast in some European countries. It remains tobe seen whether the prospect of treatingpatients suffering from serious disorders withtransplants produced by therapeutic cloningwill decrease the societal and moral resistanceto allowing the generation of embryos for`instrumental' use. (shrink)
This theoretical integration of social psychology’s main cognitive and affective constructs was shaped by 3 influences: (a) recent widespread interest in automatic and implicit cognition, (b) (...) class='Hi'>development of the Implicit Association Test (IAT; A. G. Greenwald, D. E. McGhee, & J. L. K. Schwartz, 1998), and (c) social psychology’s consistency theories of the 1950s, especially F. Heider’s (1958) balance theory. The balanced identity design is introduced as a method to test correlational predictions of the theory. Data obtained with this method revealed that predicted consistency patterns were strongly apparent in the data for implicit (IAT) measures but not in those for parallel explicit (self-report) measures. Two additional not-yet-tested predictions of the theory are described. (shrink)
Neil Tennant (Tennant, 2005) has offered an important observation about the AGM theory of belief revision (G¨ardenfors, 1988). We attempt to restate and demonstrate his result (...) class='Hi'>in a slightly different way. Fix a formal language L that embeds sentential logic. Given K ⊆ L and ϕ ∈ L, K ⊥ ϕ denotes the class of maximally consistent subsets of K that do not imply ϕ. That is, A ∈ K ⊥ ϕ iff A ⊆ K, A |= ϕ, and there is no B ⊆ K such that B ⊃ A and.. (shrink)
The increasing demand for horticultural products for nutritional and economic purposes by lesser developed countries (LDC's) is well-documented. Technological demands of the LDC's producing horticultural (...) products is also increasing. Pesticide use is an integral component of most agricultural production, yet chemicals are often supplied without supplemental information vital for their safe and efficient implementation. Illiteracy rates in developing countries are high, making pesticide education even more challenging. For women, who perform a significant share of agricultural tasks, illiteracy rates are even higher than for men. The dilemma exists of how a developing country can improve its nutritional and economic situation without giving consideration to social and environmental consequences. (shrink)
We prove that the following are consistent with ZFC. 1. 2 ω = ℵ ω 1 + K C = ℵ ω 1 + K B = K U = ω (...) 2 (for measure and category simultaneously). 2. 2 ω = ℵ ω 1 = K C (L) + K C (M) = ω 2 . This concludes the discussion about the cofinality of K C. (shrink)
