Abstract The notion of countable well order admits an alternative definition in terms of embeddings between initial segments. We use the framework of reverse mathematics to investigate the logical strength of this definition and its connection with Fraïssé’s conjecture, which has been proved by Laver. We also fill a small gap in Shore’s proof that Fraïssé’s conjecture implies arithmetic transfinite recursion over $\mathbf {RCA}_0$ , by giving a new proof of $\Sigma ^0_2$ -induction.

Abstract Transformations of well partial orders induce functions on the ordinals, via the notion of maximal order type. In most examples from the literature, these functions are not normal, in marked contrast with the central role that normal functions play in ordinal analysis and related work from computability theory. The present paper aims to explain this phenomenon. In order to do so, we investigate a rich class of order transformations that are known as $\textsf {WPO}$-dilators. According to a first main result of this paper, $\textsf {WPO}$-dilators induce normal functions when they satisfy a rather restrictive condition, which we call strong normality. Moreover, the reverse implication holds as well, for reasonably well-behaved $\textsf {WPO}$-dilators. Strong normality also allows us to explain another phenomenon: by previous work of Freund, Rathjen and Weiermann, a uniform Kruskal theorem for $\textsf {WPO}$-dilators is as strong as $\varPi ^1_1$-comprehension, while the corresponding result for normal dilators on linear orders is equivalent to the much weaker principle of $\varPi ^1_1$-induction. As our second main result, we show that $\varPi ^1_1$-induction is equivalent to the uniform Kruskal theorem for $\textsf {WPO}$-dilators that are strongly normal.

The performance over cost ratio of last generation off the shelf devices enables the design of heterogeneous distributed computing systems capable of supporting the implementation of an immersive Virtual Reality, Internet of Things based training support architecture. In this paper we present our work in progress on a low cost distributed immersive simulation system for the training of teams by means of Virtual Reality and off the shelf mobile and prototyping devices. In this case, performance prediction is crucial, because the generation of the scenario have to be performed in real time and synchronization problems may disrupt the result. The approach is demonstrated by a prototypical case study, that consists in a distributed simulator for the interactive training of groups of people that have to coordinate to face a fire emergency, and features advanced immersivity thanks to CGI-enabled stereoscopic 360 degree 3D Virtual Reality and ad-hoc devised interaction interfaces. In particular, we focus on the subsystem that is related to a single trainee, providing a reference implementation and a performance evaluation oriented model to support the design of the complete system.