Computability and analysis: the legacy of Alan Turing

We discuss the legacy of Alan Turing and his impact on computability and analysis.Comment: 49 page

Perspectives for proof unwinding by programming languages techniques

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific essay, written for the audience of proof theorists as well as the working mathematician, is not a survey of the field, but rather a personal view of the author who hopes that it may inspire future and fellow researchers

On what I do not understand (and have something to say): Part I

This is a non-standard paper, containing some problems in set theory I have in various degrees been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me, sometimes the problems are presented with a discussion of how I have tried to solve them, and sometimes with failed tries, anecdote and opinion. So the discussion is quite personal, in other words, egocentric and somewhat accidental. As we discuss many problems, history and side references are erratic, usually kept at a minimum (``see ... '' means: see the references there and possibly the paper itself). The base were lectures in Rutgers Fall'97 and reflect my knowledge then. The other half, concentrating on model theory, will subsequently appear

Laver and set theory

In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip

Assembly and Disassembly Planning by using Fuzzy Logic & Genetic Algorithms

The authors propose the implementation of hybrid Fuzzy Logic-Genetic Algorithm (FL-GA) methodology to plan the automatic assembly and disassembly sequence of products. The GA-Fuzzy Logic approach is implemented onto two levels. The first level of hybridization consists of the development of a Fuzzy controller for the parameters of an assembly or disassembly planner based on GAs. This controller acts on mutation probability and crossover rate in order to adapt their values dynamically while the algorithm runs. The second level consists of the identification of theoptimal assembly or disassembly sequence by a Fuzzy function, in order to obtain a closer control of the technological knowledge of the assembly/disassembly process. Two case studies were analyzed in order to test the efficiency of the Fuzzy-GA methodologies