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 SF2AC, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Pi-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].
On a positive set theory with inequality
LENZI, Giacomo
2011
Abstract
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 SF2AC, where atoms and coatoms are allowed. To construct the model we use an enumeration “almost without repetitions” of the Pi-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].File in questo prodotto:
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