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VcCc
PPQ classification of non-well-foundedn sets and an application ̃A
uXgNgF

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.

PPR Nonstandard Fourier transformation and Feynman path integral ̃A
uXgNgF

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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