Maximality Principles in the Hyperuniverse Programme

Foundations of Science 28 (1):287-305 (2020)
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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 (HP) 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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Naturalism in mathematics.Penelope Maddy - 1997 - New York: Oxford University Press.
The potential hierarchy of sets.Øystein Linnebo - 2013 - Review of Symbolic Logic 6 (2):205-228.
The iterative conception of set.George Boolos - 1971 - Journal of Philosophy 68 (8):215-231.

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