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On categories generalizing universal domains

Published online by Cambridge University Press:  01 April 1999

VĚRA TRNKOVÁ  and
JIŘÍ VELEBIL
VĚRA TRNKOVÁ
Affiliation:
Mathematical Institute, Charles University, Sokolovská 83, 180 00 Prague 8, Czech Republic. Email: trnkova@karlin.mff.cuni.cz
JIŘÍ VELEBIL
Affiliation:
Department of Mathematics, FEL ČVUT, Technická 2, 166 28 Prague 6, Czech Republic. Email: velebil@math.feld.cvut.cz
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Abstract

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Scott domains, originated and commonly used in formal semantics of computer languages, were generalized by J. Adámek to Scott complete categories. We prove that the categorical counterpart of the result of D. Scott – the existence of a countable based Scott domain universal with respect to all countably based Scott domains – is no longer valid for the categorical generalization. However, all obstacles disappear if the notion of the Scott complete category is weakened to a categorical counterpart of bifinite domains.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 9 , Issue 2 , April 1999 , pp. 159 - 175
Copyright
1999 Cambridge University Press

Footnotes

Both authors gratefully acknowledge the financial support of the Grant Agency of the Czech Republic under the grant No. 201/96/0119.