2nd International Conference on Physics
Siedlce University of Natural Sciences and Humanities, Poland
Title: Computation within models of ZF minus the postulate of infinity
Biography: Eliza Wajch
A significant progress in the development of an axiomatic quasi–set theory (QST) and its application in quantum physics, where indistinguishability and non-individuality appears has been made by Décio Krause and others. I offer a sketch of a modification of QST to quasi-classes theory (QCT) such that proper quasi-classes can be considered as existing objects, while ZF minus the postulate of infinity can be treated as a sub theory of QCT. It is not claimed that infinite collections certainly exist in QCT. None of the known forms of the axiom of choice is an axiom of QCT. Every quasi-set of QCT is a quasi-class of QCT. To avoid inconsistencies, it is assumed that a quasi-class which is not a quasi-set cannot be an element of a quasi-class. Notions of D-countability and D-uncountability that need not refer to numbers can be considered in QCT. The primitive concept of a quasi-cardinal (qc) in QST can be investigated deeper in QCT than in QST. Intuitively, qc (x) is a cardinal number of ZFC which is assigned to a quasi-set x to stand for the ‘quantity’ of elements of x. New arguments that the concept of qc is not precise enough have been found recently. Modifications of qc are needed to give more satisfactory answers to questions about, in a sense, how large a quasi-set can be and how many elements it can have.