Displaying similar documents to “Minimality in the Δ 1 2 -degrees”

The enriched stable core and the relative rigidity of HOD

Sy-David Friedman (2016)

Fundamenta Mathematicae

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In the author's 2012 paper, the V-definable Stable Core 𝕊 = (L[S],S) was introduced. It was shown that V is generic over 𝕊 (for 𝕊-definable dense classes), each V-definable club contains an 𝕊-definable club, and the same holds with 𝕊 replaced by (HOD,S), where HOD denotes Gödel's inner model of hereditarily ordinal-definable sets. In the present article we extend this to models of class theory by introducing the V-definable Enriched Stable Core 𝕊* = (L[S*],S*). As an application...

Minimality of non-σ-scattered orders

Tetsuya Ishiu, Justin Tatch Moore (2009)

Fundamenta Mathematicae

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We will characterize-under appropriate axiomatic assumptions-when a linear order is minimal with respect to not being a countable union of scattered suborders. We show that, assuming PFA⁺, the only linear orders which are minimal with respect to not being σ-scattered are either Countryman types or real types. We also outline a plausible approach to demonstrating the relative consistency of: There are no minimal non-σ-scattered linear orders. In the process of establishing these results,...