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International Studies in Phenomenology and Philosophy

Book | Chapter

179396

The search for new axioms in the hyperuniverse programme

Claudio Ternullo Sy David Friedman

pp. 161-183

Abstract

The Hyperuniverse Programme, introduced in Arrigoni and Friedman (Bull Symb Log 19(1):77–96, 2013), fosters the search for new set-theoretic axioms. In this paper, we present the procedure envisaged by the programme to find new axioms and the conceptual framework behind it. The procedure comes in several steps. Intrinsically motivated axioms are those statements which are suggested by the standard concept of set, i.e. the "maximal iterative concept', and the programme identifies higher-order statements motivated by the maximal iterative concept. The satisfaction of these statements ((mathbb {H})-axioms) in countable transitive models, the collection of which constitutes the "hyperuniverse' ((mathbb {H})), has remarkable first-order consequences, some of which we review in Sect. 5.

Publication details

Published in:

Antos Carolin, Honzik Radek, Ternullo Claudio, Friedman Sy David (2018) The hyperuniverse project and maximality. Dordrecht, Springer.

Pages: 161-183

DOI: 10.1007/978-3-319-62935-3_8

Full citation:

Ternullo Claudio, Friedman Sy David (2018) „The search for new axioms in the hyperuniverse programme“, In: C. Antos, R. Honzik, C. Ternullo & S. Friedman (eds.), The hyperuniverse project and maximality, Dordrecht, Springer, 161–183.