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On a positive set theory with inequality

✍ Scribed by Giacomo Lenzi

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
95 KB
Volume
57
Category
Article
ISSN
0044-3050

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✦ Synopsis

We introduce a quite natural Frege-style set theory, which we call Strong-Frege-2 (SF2 ), a sort of simplification of the theory considered in [13] (under the name Strong-Frege-3) and [1] (under the name F2). We give a model of a weaker variant of SF2 , called SF2 AC, where atoms and coatoms are allowed.

To construct the model we use an enumeration "almost without repetitions" of the Ξ  1 1 sets of natural numbers; such an enumeration can be obtained via a classical priority argument much in the style of [5] and [15].

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