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On topological set theory
Author(s) -
Libert Thierry,
Esser Olivier
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200410026
Subject(s) - mathematics , topological space , set (abstract data type) , universal set , set theory , characterization (materials science) , cantor set , natural (archaeology) , topology (electrical circuits) , pure mathematics , computer science , combinatorics , physics , archaeology , optics , history , programming language
This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)