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 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 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 internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure 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).

nLab > Latest Changes: Kripke-Joyal semantics

Bottom of Page

1 to 9 of 9

  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeMay 21st 2018

    I added the suggestion that there is a version for HoTT.

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorThomas Holder
    • CommentTimeJun 29th 2020

    Added references to

    • Anders Kock, Universal Projective Geometry via Topos Theory , JPAA 9 (1976) pp.1-24.

    • Anders Kock, Elementwise semantics in categories with pull-backs , arXiv:2004.14731 (2020). (abstract)

    diff, v20, current

    • CommentRowNumber3.
    • CommentAuthorjulia9367
    • CommentTimeApr 17th 2022
    • (edited Apr 17th 2022)

    I think it would be nice to add the specialisation of sheaf semantics for any topos of sheafs of sets on a site. In this case we have nice concrete interpretations of the logic. E.g.:

    • it suffices to consider generalized elements of the form x∈ℱ(U)x \in \mathcal{F}(U)
    • any formula is true if it is true on an open cover
    • ⇒\implies = implies on all open subsets
    • ¬\neg = false on all open subsets
    • ¬¬\neg\neg = false that (it is false on all open subsets) of all open subsets = true on a dense open subset

    [1] is a beautiful application of this to scheme theory simplifying many statements and proofs.

    [1]: Using the internal language of toposes in algebraic geometry, Ingo Blechschmidt, https://arxiv.org/abs/2111.03685

    • CommentRowNumber4.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    added K-J for HoTT by Awodey, Gambino, Hazratpour, 2022.

    diff, v25, current

    • CommentRowNumber5.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    fixing citation

    diff, v25, current

    • CommentRowNumber6.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    citation

    diff, v25, current

    • CommentRowNumber7.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    citation

    diff, v25, current

    • CommentRowNumber8.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    fixed citation

    diff, v25, current

    • CommentRowNumber9.
    • CommentAuthorsteveawodey
    • CommentTimeApr 29th 2023

    done

    diff, v25, current

1 to 9 of 9

  1.