In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L, is a particular class of sets that can be described entirely in terms of simpler sets. L is the union of the constructible hierarchy Lα . It was introduced by Kurt Gödel in his 1938 paper "The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis". In this paper, he proved that the constructible universe is an inner model of ZF set theory (that is, of Zermelo–Fraenkel set theory with the axiom of choice excluded), and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result. (Wikipedia).
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From playlist Science Unplugged: Big Ideas
What the heck is a Multiverse?
The idea of a multiverse (short for multiple universes) can seem absurd. After all, the definition of universe means everything, so what does it mean to have multiple universes? In this video, Fermilab’s Dr. Don Lincoln lists a couple possible definitions for a multiverse. The reality in
From playlist Speculative Physics
If the universe is spatially infinite, what can we say about reality...
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From playlist Science Unplugged: Cosmology
The multiverse hypothesis: Is our universe the only one?
Support me on Patreon: https://www.patreon.com/Sabine In the past decades, the idea that our universe is only one of many, has become popular among physicists. If there are several universes, their collection is called the “multiverse”, and physicists have a few theories for this that I e
From playlist Physics
What is the Universe expanding into?
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From playlist Science Unplugged: Cosmology
What is the shape of the universe?
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From playlist Science Unplugged: Cosmology
If there are multiple universes, could there be copies of us in some of them?
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From playlist Science Unplugged: Cosmology
One of the most outlandish ideas in modern physics is the multiverse - the idea that there exist multiple universes. Given that scientists tend to be fairly conservative and that this idea seems like a such a reach, it is natural to wonder why this idea is seriously discussed in leading s
From playlist Speculative Physics
How Big is the Universe? Part 1 of 2
An explanation of the size of the observable universe and why we cannot see beyond it. together with a forward look to a time when distant galaxies will no longer be visible.
From playlist Cosmology
Emily Riehl: On the ∞-topos semantics of homotopy type theory: The simplicial model of...- Lecture 2
HYBRID EVENT Recorded during the meeting "Logic and Interactions" the February 22, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual M
From playlist Topology
Yonatan harpaz : The universal property of topological Hochschild homology
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Wolfram Physics Project: a Conversation on Current Work (Jan. 26, 2021)
This is a Wolfram Physics Project conversation on our continuing efforts to make progress on the fundamental theory of physics. Begins at 3:00 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Ch
From playlist Wolfram Physics Project Livestream Archive
Axel Osmond - The over-topos at a model
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Slides: https://aroundtoposes.com/wp-content/uploads/2021/07/OsmondSlidesToposesOnline.pdf For a model of a geometric theory in a Grothendieck topos, we can construct the over-t
From playlist Toposes online
Wolfram Physics Project: Working Session Tuesday, July 28, 2020 [Metamathematics | Part 3]
This is a Wolfram Physics Project progress update at the Wolfram Summer School. This is a continuation of part two found here: https://youtu.be/ndtLa0BhEdg Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.
From playlist Wolfram Physics Project Livestream Archive
Univalent Foundations Seminar - Steve Awodey
Steve Awodey Carnegie Mellon University; Member, School of Mathematics November 19, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Cohomological Field Theories from GLSMs (Lecture 2) by David Favero
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
Formal Abstract Homotopy Theory - Jeremy Avigad
Jeremy Avigad Carnegie Mellon University February 28, 2013 For more videos, visit http://video.ias.edu
From playlist Mathematics
Axioms of Constructive Set Theory Explained
In this video we're going to discuss the various axiom schemes of constructive set theories and how they relate to type theory. I cover BCST, ECST, IKP, KPI, KP, CST, CZF, IZF, Mac Lane, Z and variants equi-consistent to ETCS from category theory, and then of course ZF and ZFC. The text I
From playlist Logic
Measurement based unitary designs and some applications - D. Markham - Workshop 2 - CEB T2 2018
Damian Markham (LIP6, CNRS, Sorbonne Université) / 05.06.2018 Measurement based unitary designs and some applications Sampling unitaries uniformly from the Haar measure has many applications across quantum information and quantum physics, including benchmarking, private channels, modelli
From playlist 2018 - T2 - Measurement and Control of Quantum Systems: Theory and Experiments
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics