technological know-how comprises descriptions of the realm we are living in. It additionally is determined by nature showing what we will be able to top describe as a excessive aLgorithmic content material. The subject operating via this number of papers is that of the interplay among descriptions, within the type of formal theories, and the algorithmic content material of what's defined, specifically of the versions of these theories. This looks such a lot explicitly right here in a couple of helpful, and great, contributions to what has until eventually lately been referred to as 'recursive version conception' - a space within which researchers from the previous Soviet Union (in specific Novosibirsk) were pre-eminent. There also are articles excited by the computability of elements of everyday mathematical buildings, and - a go back to this kind of uncomplicated underlying questions thought of through Alan Turing within the early days of the topic - a piece of writing giving a brand new viewpoint on computability within the genuine global. And, after all, there also are articles excited about the classical idea of computability, together with the 1st generally on hand survey of labor on quasi-reducibility. The participants, all across the world recognized specialists of their fields, were linked to the three-year INTAS-RFBR study venture "Com­ putability and versions" (Project No. 972-139), and such a lot have participated in a single or extra of many of the foreign workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch actions of the network.