Constructive set theory and Brouwerian principles

The paper furnishes realizability models of constructive Zermelo-Fraenkel set theory, CZF, which also validate Brouwerian principles such as the axiom of continuous choice (CC), the fan theorem (FT), and monotone bar induction (BIM), and thereby determines the proof-theoretic strength of CZF augmented by these principles. The upshot is that CZF+CC+FT possesses the same strength as CZF, or more precisely, that CZF+CC+FTis conservative over CZF for 02 statements of arithmetic, whereas the addition of a restricted version of bar induction to CZF (called decidable bar induction, BID) leads to greater proof-theoretic strength in that CZF+BID proves the consistency of CZF

Beyond old economy - new economy dualism: Urban embeddedness of current innovation processes

Current research on spatial embeddedness of the "New Economy" clearly demonstrates the use of diverse urban assets for the emerging branch. One frequent shortcoming is, however, a simplified idea of multimedia and internet enterprises as a counter-world to the traditional economy. We argue that the multitude of service companies dealing with Internet- and Multimedia applications should be considered as part of a comprehensive economic innovation process: Small, flexible and venturesome enterprises test new technology applications for economic purposes, sometimes successfully, sometimes without success. Future steps in this innovation process can be observed already: With increasing security about the economic use of new media technologies, more and more "traditional" enterprises integrate multimedia, internet and e-commerce in their daily work. What has been the domain of service enterprises will be more and more integrated in their former clients' corporations. Nevertheless, parts of multimedia and internet application might still require highly specialized skills, thus offering a basis for independent service companies even in the future. During the first phase of the innovation process, specific assets of the city have proved to be useful as research on urban and regional embeddedness of new media enterprises has shown. It seems as if traditional enterprises - instead of undertaking this step of innovation by themselves - have entrusted this trial-and-error process to an urban milieu, characterised by its creativity, its capacity to link diverse experts and its capacity to deal with uncertainty. Thus, an institutional choice has been made in order to externalize insecurity about the economic use of new technologies. The paper aims at linking the Schumpeterian innovation cycle approach and its application to regional development to the emergence of new media based industry and its links to the traditional economy. This approach should permit to go beyond the "new economy"-"old economy" dualism in order to reveal the underlying comprehensive innovative process. The centre of interest remains the urban and regional embeddedness of the current process, that is to say, the contribution of space to innovation. Based on case studies on the Hamburg metropolitan economy, its "new economy" and its increasing links between "new" and "old economy", we intend to illustrate the specific institutional form of the current innovation process in an urban context.

Reverse mathematics and well-ordering principles

The paper is concerned with generally Pi^1_2 sentences of the form 'if X is well ordered then f(X) is well ordered', where f is a standard proof theoretic function from ordinals to ordinals. It has turned out that a statement of this form is often equivalent to the existence of countable coded omega-models for a particular theory T_f whose consistency can be proved by means of a cut elimination theorem in infinitary logic which crucially involves the function f. To illustrate this theme, we shall focus on the well-known psi-function which figures prominently in so-called predicative proof theory. However, the approach taken here lends itself to generalization in that the techniques we employ can be applied to many other proof-theoretic functions associated with cut elimination theorems. In this paper we show that the statement 'if X is well ordered then 'X0 is well ordered' is equivalent to ATR0. This was first proved by Friedman, Montalban and Weiermann [7] using recursion-theoretic and combinatorial methods. The proof given here is proof-theoretic, the main techniques being Schuette's method of proof search (deduction chains) [13], generalized to omega logic, and cut elimination for infinitary ramified analysis

A system to enrich for primitive streak-derivatives, definitive endoderm and mesoderm, from pluripotent cells in culture

Two lineages of endoderm develop during mammalian embryogenesis, the primitive endoderm in the pre-implantation blastocyst and the definitive endoderm at gastrulation. This complexity of endoderm cell populations is mirrored during pluripotent cell differentiation in vitro and has hindered the identification and purification of the definitive endoderm for use as a substrate for further differentiation. The aggregation and differentiation of early primitive ectoderm-like (EPL) cells, resulting in the formation of EPL-cell derived embryoid bodies (EPLEBs), is a model of gastrulation that progresses through the sequential formation of primitive streak-like intermediates to nascent mesoderm and more differentiated mesoderm populations. EPL cell-derived EBs have been further analysed for the formation of definitive endoderm by detailed morphological studies, gene expression and a protein uptake assay. In comparison to embryoid bodies derived from ES cells, which form primitive and definitive endoderm, the endoderm compartment of embryoid bodies formed from EPL cells was comprised almost exclusively of definitive endoderm. Definitive endoderm was defined as a population of squamous cells that expressed Sox17, CXCR4 and Trh, which formed without the prior formation of primitive endoderm and was unable to endocytose horseradish peroxidase from the medium. Definitive endoderm formed in EPLEBs provides a substrate for further differentiation into specific endoderm lineages; these lineages can be used as research tools for understanding the mechanisms controlling lineage establishment and the nature of the transient intermediates formed. The similarity between mouse EPL cells and human ES cells suggests EPLEBs can be used as a model system for the development of technologies to enrich for the formation of human ES cell-derived definitive endoderm in the future.Sveltana Vassilieva, Hweee Ngee Goh, Kevin X. Lau, James N. Hughes, Mary Familari, Peter D. Rathjen and Joy Rathje

Intensity of Time and Income Interdependent Multidimensional Poverty: Well-Being and Minimum 2DGAP ; German Evidence

Extending the traditional income poverty concept by multidimensional poverty has been of growing interest within the last years. This paper contributes with an analysis of interdepend-ent multidimensional (IMD) poverty intensity of time and income, which in particular restricts social participation. The interdependency of the multiple poverty dimensions under a strong (union approach) and weak focus axiom (compensation approach) are regarded in particular when measuring the intensity of multidimensional poverty. In addition to various poverty gap measures including the multidimensional well-being gap, for the first time we propose a minimum multidimensional poverty gap (2DGAP).. - To respect Sen's capability approach with its social participation aspects we define the time dimension as genuine personal leisure time. Based on a CES well-being function and a multi-dimensional poverty line evaluated by the German population (estimated with the German Socio-Economic Panel) the individual poverty intensity of the active population is analysed for various regimes of multiple poverty. For this purpose the German Time Use Surveys 1991/92 and 2001/02 and its time use diary data are used. Analysing the active population this paper contributes too to the poverty situation of the working poor. . - All the empirical results, including the microeconometric Heckman type estimation of the IMD poverty intensity (2DGAP) and the IMD poverty risk, indicate the overall importance of the time dimension with its social participation aspect incorporated within an interdependent multidimensional time and income poverty approach. An important dimension would be ne-glected in the poverty analysis and in targeted poverty policies if time additional to income would is not respected.Intensity of time and income poverty, interdependent multidimensional time and income poverty, union and compensation approach, minimum multidimensional poverty gap (2DGAP), extended economic well-being, satisfaction/happiness, working poor

Time and Income Poverty: An Interdependent Multidimensional Poverty Approach with German Time Use Diary Data

Income as the traditional one dimensional measure in well-being and poverty analyses is extended in recent studies by a multidimensional poverty concept. Though this is certainly a progress, however, two important aspects are missing: time as an important dimension and the interdependence of the often only separately counted multiple poverty dimensions. Our paper will contribute to both aspects: First, we consider time - and income - both as striking and restricting resources of everyday activities and hence account for time and income as important multiple poverty dimensions. Second, the interdependence of the poverty dimensions will be evaluated by the German population to allow an advanced approach to understand possible substitution effects and the respective trade offs between the dimensions. Referring to the time dimension, we follow Sen's capability approach with its freedom of the living conditions' choice and social exclusion and argue, that restricted time might exclude from social participation. In particular, restricted genuine, personal leisure time (not entire leisure time) in particular is associated with a restricted social participation. The crucial question then is how to measure the substitution between income and such genuine leisure time. In our analysis we consider the country population's valuation with data from the German Socio-Economic Panel and estimate the substitution by a CES-utility function of general utility/satisfaction. Given this quantification we disentangle time, income and interdependent multidimensional poverty regimes characterising the working poor. In addition, we quantify further socio-economic influences for each interdependent multidimensional poverty regime by a multinomial logit based on time use diary data of the German Time Use Study 2001/02. One striking result for Germany: the substitution between time and income is significant and we find an important fraction of time poor who are unable to substitute their time deficit by income. These poor people are ignored within the poverty and well-being as well as the time crunch and time famine discussion so far.Interdependent multidimensional time and income poverty, time and income substitution, extended economic well-being, satisfaction, CES utility function estimation, working poor, German Socio-Economic Panel, German Time Use Surveys 2001/02