Educational Expansion and Persistent Inequalities of Education: Utilizing the Subjective Expected Utility Theory to Explain the Increasing Participation Rates in Upper Secondary School in the Federal Republic Of Germany

This investigation attempts to answer the question why more and more parents have chosen the Gymnasium for their children's secondary school education in post‐war West Germany. Based on the theory of subjective expected utility, the crucial mechanisms of parental educational decisions have been emphasized. From this perspective it is assumed that increasing educational motivation coupled with changes in the subjective evaluation of the cost–benefit of education were important conditions for an increasing participation in upper secondary schools. These were, however, in turn, the result of educational expansion. The empirical analyses for three time‐periods in the 1960s, 1970s, and 1980s confirm these assumptions to a large degree. Additionally, empirical evidence was found to suggest that in addition to the intentions of parents and the educational career of their children, structural moments of educational expansion and their own inertia played an important role in the pupils' transition from one educational level to the next. Finally, evidence was found that persistent class‐specific educational inequality stems from a constant balance in the relative cost–benefit advantages between social classes as well as from an increasing difference of primary origin effect between social classes in the realization of their educational choice.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

Explicit mathematics and operational set theory: some ontological comparisons

We discuss several ontological properties of explicit mathematics and operational set theory: global choice, decidable classes, totality and extensionality of operations, function spaces, class and set formation via formulas that contain the definedness predicate and applications.