Vicious Queues and Vicious Circles

Raja Natarajan (School of Technology & Computer Science, Tata Institute of Fundamental Research)

DATE: 2009-10-09
TIME: 14:00:00 - 15:00:00
LOCATION: RSISE Seminar Room, ground floor, building 115, cnr. North and Daley Roads, ANU

ABSTRACT:
We will describe some of the preliminary results from an ongoing research program to reconstruct the proofs of fundamental theorems in logic using a minimal repertoire of basic constructs and reasoning mechanisms. In particular we shall examine an array of paradoxes for the kind of constructs they employ, and use them as a guide to re-examine the proof of Cantor's theorem in set theory. We shall present two uncommon proofs of Cantor's theorem in set theory. In addition to being novel, the proofs that we discuss will differ from the most well known proofs of Cantor's theorem in an important way. Notable features include the way in which in which one of them makes use of the notion of negation, and also the dual relationship that the two proofs share with each other.

BIO:
Raja Natarajan is a faculty member in the School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India. He completed his Master's degree at the Indian Institute of Science, Bangalore, India, and his Ph.D. at the Tata Institute of Fundamental Research. He has held visiting positions at the University of Nijmegen, Netherlands; EPFL, Switzerland, and the University of Paris-7, France. He is a memeber of the editorial board of the journal ``Logica Universalis'', and a guest editor of ``Sadhana'' -- the Engineering Journal of the Indian Academy of Sciences. His research interests include Type theory and Interactive Theorem Proving, Formal Methods, and Models of Interacting Processes. More details of his research activities may be found on his homepage: http://www.tcs.tifr.res.in/~raja

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