Solving equations in the universe of hypersets

Date
1993
Advisor
Akman, Varol
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Bilkent University
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Language
English
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Thesis
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Abstract

Hyperset Theory (a.k.a. ZFC~/AFA) of Peter Aczel is an enrichment of the classical ZFC set theory and uses a graphical representation for sets. By allowing non-well-founded sets, the theory provides an appropriate framework for modeling various phenomena involving circularity. Z F C /A F A has an important consequence that guarantees a solution to a set of equations in the universe of hypersets, viz. the Solution Lemma. This lemma asserts that a system of equations defined in the universe of hypersets has a unique solution, and has applications in areas like artificial intelligence, database theory, and situation theory. In this thesis, a program called HYPERSOLVER, which can solve systems of equations to which the Solution Lemma is applicable and which has built-in procedures to display the graphs depicting the solutions, is presented.

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Keywords
Set Theory, ZFC, Non-well-founded Sets, Hyperset Theory (ZFC“ /AFA), Solving Equations, The Solution Lemma
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Published Version (Please cite this version)