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.