578 research outputs found
On what I do not understand (and have something to say): Part I
This is a non-standard paper, containing some problems in set theory I have
in various degrees been interested in. Sometimes with a discussion on what I
have to say; sometimes, of what makes them interesting to me, sometimes the
problems are presented with a discussion of how I have tried to solve them, and
sometimes with failed tries, anecdote and opinion. So the discussion is quite
personal, in other words, egocentric and somewhat accidental. As we discuss
many problems, history and side references are erratic, usually kept at a
minimum (``see ... '' means: see the references there and possibly the paper
itself).
The base were lectures in Rutgers Fall'97 and reflect my knowledge then. The
other half, concentrating on model theory, will subsequently appear
Deformations of quantum field theories on de Sitter spacetime
Quantum field theories on de Sitter spacetime with global U(1) gauge symmetry
are deformed using the joint action of the internal symmetry group and a
one-parameter group of boosts. The resulting theory turns out to be wedge-local
and non-isomorphic to the initial one for a class of theories, including the
free charged Dirac field. The properties of deformed models coming from
inclusions of CAR-algebras are studied in detail.Comment: 26 pages, no figure
Nets, relations and linking diagrams
In recent work, the author and others have studied compositional algebras of
Petri nets. Here we consider mathematical aspects of the pure linking algebras
that underly them. We characterise composition of nets without places as the
composition of spans over appropriate categories of relations, and study the
underlying algebraic structures.Comment: 15 pages, Proceedings of 5th Conference on Algebra and Coalgebra in
Computer Science (CALCO), Warsaw, Poland, 3-6 September 201
Power operations in -theory completed at a prime
We describe the action of power operations on the -completed cooperation
algebras K^\vee_0 K = K_0(K)\sphat_p for -theory at a prime~, and
K^\vee_0 KO = K_0(KO)\sphat_2.Comment: Version 6: final update, to appear in special issue of the Tbilisi
Mathematical Journal on Homotopy Theory, Spectra, and Structured Ring Spectr
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