Slow consistency

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Slow consistency

The fact that “natural” theories, i.e. theories which have something like an “idea” to them, are almost always linearly ordered with regard to logical strength has been called one of the great mysteries of the foundation of mathematics. However, one easily establishes the existence of theories with incomparable logical strengths using self-reference (Rosser-style). As a result, PA + Con(PA) is ...

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Slow brain potentials in a visual-spatial memory task: topographic distribution and inter-laboratory consistency.

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Long Sequences of Descending Theories and other Miscellenia on Slow Consistency∗

For a provably recursive function f : N→ N of PA one can consider the notion of f -consistency for PA, Conf (PA) := ∀xCon(PA f(x)), where PA k denotes the fragment of PA with induction restricted to Σk formulae. It was shown in [8] that for a certain slow growing function f the strength of PA + Conf (PA) lies strictly between PA and PA + Con(PA). Letting τBH be the Bachmann-Howard ordinal, this...

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Approximate Consistency Condition from Running Spectral Index in Slow-Roll Inflationary Models

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ژورنال

عنوان ژورنال: Annals of Pure and Applied Logic

سال: 2013

ISSN: 0168-0072

DOI: 10.1016/j.apal.2012.11.009