Proving Peano Arithmetic with Set Theory (Series Intro)

An introduction to the third month of set theory and higher order logic on Peano Arithmetic. This month we will be proving the five Peano Postulates, and introducing the axiom of infinity. Sponsors: NBA_Ruby, Antybodi, Federico Galvão, Mike Gloudemans, Andy Capone, Andreas Froestl, The Jack Bancroft, Jakey, Andrew Sullivan, Eugene SY, Tyler James, Antoinemp1, Dennis Sexton, Joao Sa, Joshua Furman, SirSpammenot Multitude, Ploney, Avatar, Diéssica, GhostlyYorick, Hendrick McDonald, horace chan, Will DeRousse, Star Gazer, Paul Linkogle, Julian Seidl, Doǧan Çetin, Thomas Kristic, Panos Tsivi, Jesse Willette and Daniel West. Thanks for your support on Patreon! If you want to become a patron, follow this link: https://www.patreon.com/Carneades Here are some videos you might enjoy: The 100 Days of Logic (https://youtube.com/playlist?list=PLz0n_SjOttTcjHsuebLrl0fjab5fdToui) History of Philosophy (https://youtube.com/playlist?list=PLz0n_SjOttTc3DVJVu-A7Oz9PPSR2eCN5) Ancient Philosophers & Zeno’s Paradoxes (https://youtube.com/playlist?list=PLz0n_SjOttTe34Mjc1e2ar_qqpMqcpxvv) ExPhi Experimental Philosophy (https://www.youtube.com/channel/UCa9HhN3Obz4xq_jyPlZE_lw) Map of Philosophy (https://www.youtube.com/watch?v=YxBShJU_CKs) More videos with Carneades (https://www.youtube.com/channel/UC1VzCyqpmCaRh8_BnijbOvg) Philosophy by Topic: Epistemology: https://youtube.com/playlist?list=PLz0n_SjOttTc2k5SeO8VJYS_Yl9THy6cM Metaphysics: https://youtube.com/playlist?list=PLz0n_SjOttTeXRZhIv0tr-dWiG2NQJ9jT Political Philosophy: https://youtube.com/playlist?list=PLz0n_SjOttTfaixflq-_HpB60jNz9uFJt Philosophy of Religion: https://youtube.com/playlist?list=PLz0n_SjOttTcrnflyetSnrzk_hWOPtzCe Ancient Philosophy: https://youtube.com/playlist?list=PLz0n_SjOttTcBISYZ7mSQVzPizR17dQGh Philosophy of Science: https://youtube.com/playlist?list=PLz0n_SjOttTf9XmTQncrxtuWPEvXN9vUC Philosophy of Language: https://youtube.com/playlist?list=PLz0n_SjOttTeQkp6SFbnWjluJXUUvZK7n Philosophy of Art/Aesthetics: https://youtube.com/playlist?list=PLz0n_SjOttTfJ-FYWvSButSSRYjAc_4ps Buy stuff with Zazzle: https://www.zazzle.com/store/carneades?rf=238568769552007656 Follow us on Twitter: @CarneadesCyrene https://twitter.com/CarneadesCyrene 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, The Oxford Companion to Philosophy, The Routledge Encyclopedia of Philosophy, The Collier-MacMillan Encyclopedia of Philosophy, the Dictionary of Continental Philosophy, and more! (#SetTheory #PeanoArithmetic #Logic)