UA37/4 Funeral March Heroica

Sheet music for Franz Strahm\u27s original composition Funeral March Heroica written in memorial of the fallen heroes of the World War I American Expeditionary Forces

Wellordering proofs for metapredicative Mahlo

In this article we provide wellordering proofs for metapredicative systems of explicit mathematics and admissible set theory featuring suitable axioms about the Mahloness of the underlying universe of discourse. In particular, it is shown that in the corresponding theories EMA of explicit mathematics and KPm0 of admissible set theory, transfinite induction along initial segments of the ordinal φω00, for φ being a ternary Veblen function, is derivable. This reveals that the upper bounds given for these two systems in the paper Jäger and Strahm [11] are indeed shar

Partial Applicative Theories and Explicit Substitutions

Systems based on theories with partial self-application are relevant to the formalization of constructive mathematics and as a logical basis for functional programming languages. In the literature they are either presented in the form of partial combinatory logic or the partial A calculus, and sometimes these two approaches are erroneously considered to be equivalent. In this paper we address some defects of the partial λ calculus as a constructive framework for partial functions. In particular, the partial λ calculus is not embeddable into partial combinatory logic and it lacks the standard recursion-theoretic model. The main reason is a concept of substitution, which is not consistent with a strongly intensional point of view. We design a weakening of the partial λ calculus, which can be embedded into partial combinatory logic. As a consequence, the natural numbers with partial recursive function application are a model of our system. The novel point will be the use of explicit substitutions, which have previously been studied in the literature in connection with the implementation of functional programming language

Polynomial time operations in explicit mathematics

In this paper we study (self-)applicative theories of operations and binary words in the context of polynomial time computability. We propose a first order theory PTO which allows full self-application and whose provably total functions on = {0, 1}* are exactly the polynomial time computable functions. Our treatment of PTO is proof-theoretic and very much in the spirit of reductive proof theor

Epicurean Friendship: How are Friends Pleasurable?

Although the Epicurean ethical system is fundamentally egoistic and hedonistic, it attributes a surprisingly significant role to friendship. Even so, I argue that traditional discussions of Epicurean friendship fail to adequately account for the value (or pleasure) of individual friends. In this thesis I present an amended notion of Epicurean friendship that better accounts for all of the pleasure friends afford. However, the success of my project requires rejecting an Epicurean ethical principle. Because of this, I explore textual evidence both in favor and against the amended notion I propose and the problematic ethical principle. After arguing against the problematic ethical principle and dispelling additional objections to my project, I conclude that Epicureans should endorse the amended notion of friendship I have developed

Cooperative Learning: Group Processing and Students Needs for Self-Worth and Belonging

The purpose of this study was to examine students’ perceptions of the extent to which reflection, a principle of cooperative learning, satisfied their needs for self-worth and belonging. Eight mature preuniversity students completed a scaled questionnaire and took part in a focus group interview following a 12-week preliminary study into the efficacy of reflection. Students perceived reflection as contributing to the satisfaction of their needs for self-worth and belonging. They also perceived reflection as contributing to their needs for acceptance. This was unexpected and is perhaps critical, as acceptance might be a condition of effective learning. Hence this article calls for further research into reflection in relation to acceptance and the role these play in contributing to effective learning and teaching.L’objectif de cette recherche était d’étudier les perceptions des élèves quant à la mesure dans laquelle la réflexion, un principe de l’apprentissage coopératif, répondait à leurs besoins d’appartenance et d’estime de soi. Suite à une étude préliminaire de 12 semaines sur l’efficacité de la réflexion, huit élèves raisonnés préuniversitaires ont complété un questionnaire gradué et ont participé à une entrevue en tant que groupe de discussion. Les résultats indiquent que les élèves perçoivent que la réflexion répond à leurs besoins d’appartenance de d’estime de soi. De plus, ils croient que la réflexion contribue à répondre à leur besoin d’être acceptés. Ce résultat était inattendu et pourrait s’avérer crucial, l’acceptation pouvant être une condition essentielle à l’apprentissage efficace. L’auteur lance donc l’appel pour que la recherche se poursuive sur le rapport entre la réflexion et l’acceptation d’une part, et le rôle que jouent ces deux éléments dans l’apprentissage et l’enseignement efficaces d’autre part

Some theories with positive induction of ordinal strength φω0

This paper deals with: (i) the theory which results from by restricting induction on the natural numbers to formulas which are positive in the fixed point constants, (ii) the theory BON(μ) plus various forms of positive induction, and (iii) a subtheory of Peano arithmetic with ordinals in which induction on the natural numbers is restricted to formulas which are Σ in the ordinals. We show that these systems have proof-theoretic strength φω

Admissible closures of polynomial time computable arithmetic

We propose two admissible closures $${\mathbb{A}({\sf PTCA})}$$ and $${\mathbb{A}({\sf PHCA})}$$ of Ferreira's system PTCA of polynomial time computable arithmetic and of full bounded arithmetic (or polynomial hierarchy computable arithmetic) PHCA. The main results obtained are: (i) $${\mathbb{A}({\sf PTCA})}$$ is conservative over PTCA with respect to $${\forall\exists\Sigma^b_1}$$ sentences, and (ii) $${\mathbb{A}({\sf PHCA})}$$ is conservative over full bounded arithmetic PHCA for $${\forall\exists\Sigma^b_{\infty}}$$ sentences. This yields that (i) the $${\Sigma^b_1}$$ definable functions of $${\mathbb{A}({\sf PTCA})}$$ are the polytime functions, and (ii) the $${\Sigma^b_{\infty}}$$ definable functions of $${\mathbb{A}({\sf PHCA})}$$ are the functions in the polynomial time hierarch