Décio Krause

PhD Thesis

“Non_reflexivity, Indistinguishability, and Weyl’s Aggregates” (in Portuguese), Department of Philosopy, University of São Paulo (USP), 1990.

Supervisor: Newton C. A. da Costa

In this work, I developed some logic and mathematical systems that try to cope with the general ideas advanced by Erwin Schroedinger concerning the non-individuality of elementary particles in quantum mechanics. After a general discussion, partially based on Steven French’s papers on the subject, I have extended da Costa’s first order “Schroedinger Logic” to a higher-order logic (a logic of order w -simple theory of types), and proved a generalized completeness theorem (in Henkins’s sense) for such a logic. This part of the thesis was published (with Newton da Costa) in Studia Logica (look here). The main part of the work was the development of quasi-set theory, a mathematical theory which aims to deal with collections of indistinguishable objects “right from the start” (following a suggestion of Heinz Post). The corresponding chapter was published as a paper in the Notre Dame Journal of Formal Logic (look here). The thesis also contains a general discussion on the logic aspects of quantum mechanics.

Examiners:

Prof. Newton C. A. da Costa, Department of Philosophy, USP.

Prof. Jacob Zimbarg, Department of Mathematics, USP

Prof. Antonio Mario Sette, Department of Mathematics, UNICAMP

Dr. Iole de Freitas Druck, Department of Mathematics, USP

Dr. Zara Issa Abud, Department of Mathematics, USP.