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Indeterminateness and `The' Universe of Sets: Multiversism, Potentialism, and Pluralism
In Melvin Fitting (ed.), Research Trends in Contemporary Logic (Series: Landscapes in Logic). College Publications. pp. 105-182 (2021)
Abstract
In this article, I survey some philosophical attitudes to talk concerning `the' universe of sets. I separate out four different strands of the debate, namely: (i) Universism, (ii) Multiversism, (iii) Potentialism, and (iv) Pluralism. I discuss standard arguments and counterarguments concerning the positions and some of the natural mathematical programmes that are suggested by the various views.Author's Profile
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References found in this work
The exact strength of the class forcing theorem.Victoria Gitman, Joel David Hamkins, Peter Holy, Philipp Schlicht & Kameryn J. Williams - 2020 - Journal of Symbolic Logic 85 (3):869-905.
Class forcing, the forcing theorem and Boolean completions.Peter Holy, Regula Krapf, Philipp Lücke, Ana Njegomir & Philipp Schlicht - 2016 - Journal of Symbolic Logic 81 (4):1500-1530.
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