Six Months of Set Theory And Higher Order Logic

This is a brand new series which covers topics in set theory and higher order logic! There will be one month going up today, and five more coming soon!

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)

[cdo]

Six whole months of set theory!? It's a dream come true :D Thank you Carneades <3

[benthephilosopher]

When are y'all gonna make videos for second-order logic?

[philp]

I really enjoyed this series! Thank you for it. It seems like you’ve potentially changed your mind about continuing it, though? If that is the case, are there any books beyond the ones mentioned in the description to learn some of the material that was initially intended for later months? Again, thank you for piquing my interests.

[NoNTrvaL]

Will we get to Godel's incompleteness theorems? Oh and there's this cool thing called Reverse Mathematics. Check it out!

[thisismyname]

"Neumann" is pronounced like "Noyman".