This volume began as a remembrance of Alonzo Church while he was still with us and is now finally complete. It contains papers by many well-known scholars, most of whom have been directly influenced by Church's own work. Often the emphasis is on foundational issues in logic, mathematics, computation, and philosophy - as was the case with Church's contributions, now universally recognized as having been of profound fundamental significance in those areas. The volume will be of interest to logicians, computer (...) scientists, philosophers, and linguists. The contributions concern classical first-order logic, higher-order logic, non-classical theories of implication, set theories with universal sets, the logical and semantical paradoxes, the lambda-calculus, especially as it is used in computation, philosophical issues about meaning and ontology in the abstract sciences and in natural language, and much else. The material will be accessible to specialists in these areas and to advanced graduate students in the respective fields. (shrink)

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: I reaffirm and extend the notion of social autopoiesis away from mere labels and descriptions to acting physical components of social systems and societies, ranging from subcellular to biological and human. All self-producing biological organisms are essentially societies of interacting components and therefore notions of autopoiesis and social systems are fundamentally, if not definitionally, interrelated. Some examples of real-life applications (...) of social autopoiesis are also given. Future generations of scientists might even find the qualifier “social” redundant because there is no other autopoiesis than “social.”. (shrink)

This is a survey paper on the descriptive set theory of hereditary families of closed sets in Polish spaces. Most of the paper is devoted to ideals and σ-ideals of closed or compact sets.

We prove several trichotomy results for ideals of compact sets. Typically, we show that a "sufficiently rich" universally Baire ideal is either $\Pi _{3}^{0}$-hard, or $\Sigma _{3}^{0}$-hard, or else a σ-ideal.