Azriel Levy (1934–) did fundamental work in set theory when it was transmuting into a modern, sophisticated field of mathematics, a formative period of over a decade straddling Cohen’s 1963 founding of forcing. The terms “Levy collapse”, “Levy hierarchy”, and “Levy absoluteness” will live on in set theory, and his technique of relative constructibility and connections established between forcin...

A formulation of naive set theory is given in Lafont’s Soft Linear Logic, a logic with polynomial time cut-elimination. We demonstrate that the provably total functions of this set theory are precisely the PTIME functions. A novelty of this approach is the representation of the unary/binary natural numbers by two distinct sets (the safe naturals and the soft naturals).

We discuss an emerging group of successful parties in Central and Eastern "Concept Structures and Fuzzy Set Theory: A Proposal for Concept. Applying the fuzzy set theory is a good example of meaning. When viewing the areas of decision making in marketing, decision making in the business. A conceptual formulation emphasizes on the meaning and interpretation of the formulations makes an in-depth ...

Paul Erdős (26 March 1913 20 September 1996) was a mathematician par excellence whose results and initiatives have had a large impact and made a strong imprint on the doing of and thinking about mathematics. A mathematician of alacrity, detail, and collaboration, Erdős in his six decades of work moved and thought quickly, entertained increasingly many parameters, and wrote over 1500 articles, t...

In as much as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the rôle of transcendental set theory (i) in chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (Church-Turing thesi...

These lecture notes are intended to recapitulate class lectures. Several notational considerations exist. Namely, appendices to lectures generally provide information not found in the lecture, but are nonetheless helpful for producing a more rigorous understanding of the material; an * (asterisk) next to a proposition, definition, theorem, etc. indicates it was not explicitly written (or mentio...

If one is to exploit the notion of interlanguage in error diagnosis systems, a precise definition of this concept is useful. We will define interlanguage set theoretically, on two different levels. A comparison of a first language and a target language on the X^-level makes it possible to compare structural similarity between languages, and a comparison on the Vx-level enables an explication of...