Results 1 to 10 of about 4,390 (36)

Infinitesimal Structure of Singularities

Universe, 2017
Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales.
Michael Heller, Jerzy Król
doaj   +1 more source

On choice rules in dependent type theory [PDF]

, 2017
In a dependent type theory satisfying the propositions as types correspondence together with the proofs-as-programs paradigm, the validity of the unique choice rule or even more of the choice rule says that the extraction of a computable witness from an ...
Maietti, MARIA EMILIA
core   +1 more source

Unsharp Values, Domains and Topoi [PDF]

, 2011
The so-called topos approach provides a radical reformulation of quantum theory. Structurally, quantum theory in the topos formulation is very similar to classical physics.
Barbosa, Rui Soares, Doering, Andreas
core   +1 more source

Structuring co-constructive logic for proofs and refutations [PDF]

, 2016
This paper considers a topos-theoretic structure for the interpretation of co-constructive logic for proofs and refutations following. It is notoriously tricky to define a proof-theoretic semantics for logics that adequately represent constructivity over
Trafford, James
core   +2 more sources

Topos theory and `neo-realist' quantum theory

, 2007
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects.
A. Döring, B. Banaschewski, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, C. J. Isham, F. W. Lawvere, G. Birkhoff, J. L. Bell, J. Lambek, M. H. Stone, M. P. Olson, P. T. Johnstone, P. T. Johnstone, R. Goldblatt, R. V. Kadison, S. Kochen, S. M. Lane, S. M. Lane   +20 more
core   +2 more sources

Set Theory and its Place in the Foundations of Mathematics:a new look at an old question [PDF]

, 2017
This paper reviews the claims of several main-stream candidates to be the foundations of mathematics, including set theory. The review concludes that at this level of mathematical knowledge it would be very unreasonable to settle with any one of these ...
A Lévy, AA Fraenkel, B Bolzano, B Rang, C Burali-Forti, E Zermelo, E Zermelo, G Osius, H Cantor, JD Hamkins, K Gödel, K Gödel, K Kunen, P Cohen, S Awodey, S Shapiro   +15 more
core   +3 more sources

Characterizing Van Kampen Squares via Descent Data

, 2012
Categories in which cocones satisfy certain exactness conditions w.r.t. pullbacks are subject to current research activities in theoretical computer science.
A. Grothendieck, Adrian Rutle, G Janelidze, H. Ehrig, H. Ehrig, Harald König, Hartmut Ehrig, M. Barr, M. Barr, Michael Löwe, Michael Löwe, Peter Freyd, Peter Johnstone, Robert Goldblatt, S. Lack, S. Lack, T. Heindel, Thomas Soboll, Ulrike Golas, Uwe Wolter, Z. Diskin   +20 more
core   +2 more sources

Higher Theory and the Three Problems of Physics [PDF]

, 2017
According to the Butterfield--Isham proposal, to understand quantum gravity we must revise the way we view the universe of mathematics. However, this paper demonstrates that the current elaborations of this programme neglect quantum interactions.
Veilahti, Antti
core   +1 more source

Finitary Topos for Locally Finite, Causal and Quantal Vacuum Einstein Gravity

, 2005
Previous work on applications of Abstract Differential Geometry (ADG) to discrete Lorentzian quantum gravity is brought to its categorical climax by organizing the curved finitary spacetime sheaves of quantum causal sets involved therein, on which a ...
Raptis, Ioannis
core   +4 more sources

Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models [PDF]

, 2011
Operational logic and bioinformatics models of nonlinear dynamics in complex functional systems such as neural networks, genomes and cell interactomes are proposed.
I. C. Baianu
core   +1 more source