新田，岡田

１１月２日 classification of non-well-foundedn sets and an application のア

ブストラクト：

We give an algorithm for a classification of Scott

sets, and count the number of Scott sets of nodes 1,2 and 3.

Furthermore, we construct infinite descending $\in$-sequences in set

theories

including Aczel set theory, and discuss a non-standard analysis in Boffa set

theory.

１１月３日 Nonstandard Fourier transformation and Feynman path integral のア

ブストラクト：

We define an infinitesimal Fourier transformation for a functional on

an infinite dimensional function space according to

nonstandard analysis. It is some sense double

infinitesimalized, and it implies a theory of Fourier

analysis for functionals. Furthermore we rigorously reformulate Feynman

path integrals of models for nonrelativistic and relativistic quantum

electrodynamics using the infinitesimal Fourier transformation. We

prove that they correspond to a fundamental solution of a

differential equation of Schr\"odinger type but on an infinite

dimensional space and an operator of a sum of second ordered functional

derivatives.

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