Foundations of Science:1-19 (forthcoming)

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Abstract
In recent years, one of the main thrusts of set-theoretic research has been the investigation of maximality principles for V, the universe of sets. The Hyperuniverse Programme has formulated several maximality principles, which express the maximality of V both in height and width. The paper provides an overview of the principles which have been investigated so far in the programme, as well as of the logical and model-theoretic tools which are needed to formulate them mathematically, and also briefly shows how optimal principles, among those available, may be selected in a justifiable way.
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DOI 10.1007/s10699-020-09707-8
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References found in this work BETA

Naturalism in Mathematics.Penelope Maddy - 1997 - Oxford, England: Oxford University Press.
The Iterative Conception of Set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.
The Potential Hierarchy of Sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.

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