LEVEL THEORY, PART 3: A BOOLEAN ALGEBRA OF SETS ARRANGED IN WELL-ORDERED LEVELS
نویسندگان
چکیده
Abstract On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, develop boolean algebra sets arranged in well-ordered levels. I show by presenting Boolean Level Theory, which fuses Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games surreal numbers; extension is definitionally equivalent ZF.
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ژورنال
عنوان ژورنال: The Bulletin of Symbolic Logic
سال: 2021
ISSN: ['1943-5894', '1079-8986']
DOI: https://doi.org/10.1017/bsl.2021.15