Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeDec 30th 2017

    Created double-negation shift, with a proof that it is equivalent to double-negated excluded middle.

    • CommentRowNumber2.
    • CommentAuthorJonasFrey
    • CommentTimeDec 31st 2017
    • (edited Dec 31st 2017)

    If I’m not mistaken, this principle holds in the topos of sheaves on a space (or locale) XX iff XX contains a dense locally decidable open, i.e. a dense open set UO(X)U\in O(X) such that for all VUV\subseteq U we have UV¬VU\subseteq V\cup\neg V. An example is the Sierpinski space, a counterexample is the real line. (the negation is the closure of the complement)

    • CommentRowNumber3.
    • CommentAuthorJonasFrey
    • CommentTimeDec 31st 2017
    • (edited Dec 31st 2017)

    I suppose at least in the spatial case the local decidability is equivalent to discreteness, so the condition means that XX has a dense and discrete open subspace.

    An example satisfying T_2 is the 1-point compacitification of an infinite set.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeDec 31st 2017

    If you’d like to add this to the page with a proof, feel free!

    • CommentRowNumber5.
    • CommentAuthorJonasFrey
    • CommentTimeJan 2nd 2018

    Did it, at least with proof outlines. I hope I didn’t make any mistakes!

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeJan 2nd 2018

    Thanks!

    • CommentRowNumber7.
    • CommentAuthorspitters
    • CommentTimeJul 17th 2018

    DNS holds in every Kripke model with finite frame.

    diff, v5, current