The Ordinary Set Theorem (Proof) Axiomatic Set Theory

A proof that the universal class cannot be a set due to Russell's paradox, and the property of being an ordinary set.

This series covers the basics of set theory and higher order logic. In this month we are looking at the properties of sets and classes, including transitive sets, swelled sets, supercomplete sets, ordinary sets, proper subsets, null sets, empty sets, universal sets, and void sets. We are also looking at the first four axioms of a basic universe, following Neumann Berneays Gödel (NBG) set theory. In the next month we will look at relationships between sets.

Sponsors: João Costa Neto, Dakota Jones, Thorin Isaiah Malmgren, Prince Otchere, Mike Samuel, Daniel Helland, Mohammad Azmi Banibaker, Dennis Sexton, kdkdk, Yu Saburi, Mauricino Andrade, Diéssica, Will Roberts, Greg Gauthier, Christian Bay, Joao Sa, Richard Seaton, Edward Jacobson, isenshi, and √2. Thanks for your support!

Information for this video gathered from The Stanford Encyclopedia of Philosophy, The Internet Encyclopedia of Philosophy, The Cambridge Dictionary of Philosophy, The Oxford Dictionary of Philosophy, Set Theory and the Continuum Problem by Smullyan and Fitting, Set Theory The Structure of Arithmetic by Hamilton and Landin, and more! (#SetTheory)

[nineironshore]

I don't know why people are saying this a great series. You keep promising an understanding of class and set without any payoff. In fact you make the issue more complex not less.

[gutzimmumdo]

exelent as always, now i understand much better how this proving thing works and what the ideas behind it are, thank you carneades!

[creativeprocessingunitmk]

Absolutely amazing video Carneades.org as always, I’m becoming one of your biggest fans I think!

[movaxh]

Does the "ordinary set theorem" follows from axioms we are going to choose and present later, or it is just more of a preparatory theorem, to make justification of classes in axioms compelling?

Or is it more of a justification to make it an axiom itself?

[mohammedshoaib]

hi carneades can you please make a play list on mathematical symbols because I'm not understanding this

[mohammedshoaib]

Oh.I don't know how other people understand this but I was never taught logic in school. So I need a foundation.

[carlcanavan]

aka the 'Reduction Axiom' from the ZFC world (right?)

[movaxh]

So, in P8, the "Dist." is basically DeMorgan law?