25th International Symposium on Multiple-Valued Logic Finitary Approximations and Metric Structure of the Space of Clones Bloomington, Indiana May 23-May 25 ISBN: 0-8186-7118-1
Abstract: Let O/sub k/ denote the set of all multivariable functions over E/sub k/ into E/sub k/ where E/sub k/ is a k element set (k/spl ges/2). A clone over E/sub k/ is a subset of O/sub k/ which is closed under composition. The set L/sub k/ of all clones over E/sub k/ is called the clone space. The structure of L/sub 2/ is completely known since E.L. Post (1941), but for k/spl ges/3, the structure of L/sub k/ seems extremely complicated and is still mostly unknown. In order to get a better perspective on L/sub k/, we firstly propose to define finitary approximation of L/sub k/, which is some simplified structure of L/sub k/. Then, motivated by this concept, a metric function is introduced into the clone space L/sub k/. As a metric space, L/sub k/ is shown to have such properties as completeness, totally boundedness and compactness. Moreover, it is shown that if a clone C is an isolated point in L/sub k/, it is finitely generated.
Index Terms:
set theory; formal logic; finitary approximations; metric structure; space of clones; multivariable functions; finitary approximation; clone space; metric function; completeness; totally boundedness; compactness; isolated point
Citation:
H. Machida, "Finitary Approximations and Metric Structure of the Space of Clones," ismvl, pp.0200, 25th International Symposium on Multiple-Valued Logic, 1995 Usage of this product signifies your acceptance of the Terms of Use. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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