455 research outputs found
The Wonder of Colors and the Principle of Ariadne
The Principle of Ariadne, formulated in 1988 ago by Walter Carnielli
and Carlos Di Prisco and later published in 1993, is an infinitary principle that is independent of the Axiom of Choice in ZF, although it can be consistently added to
the remaining ZF axioms. The present paper surveys, and motivates, the foundational importance of the Principle of Ariadne
and proposes the Ariadne Game, showing that the Principle of Ariadne,
corresponds precisely
to a winning strategy for the Ariadne Game. Some relations to other
alternative. set-theoretical principles
are also briefly discussed
Group field theory condensate cosmology: An appetizer
This contribution is an appetizer to the relatively young and fast evolving
approach to quantum cosmology based on group field theory condensate states. We
summarize the main assumptions and pillars of this approach which has revealed
new perspectives on the long-standing question of how to recover the continuum
from discrete geometric building blocks. Among others, we give a snapshot of
recent work on isotropic cosmological solutions exhibiting an accelerated
expansion, a bounce where anisotropies are shown to be under control and
inhomogeneities with an approximately scale-invariant power spectrum. Finally,
we point to open issues in the condensate cosmology approach.Comment: Review article as an invited contribution for the special issue
"Progress in Group Field Theory and Related Quantum Gravity Formalisms",
Universe journa
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