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Great video easy to follow

0:32 :( 1:42 :)

At 9:45 , we dont need to take the union with C0 or C1 C2 C3 in any of the following steps, its redundant since in the end when we will take union of C0 C1 C2 we would include all that we had needed, correct me if I am wrong please.

Sir, do you suggest Elliott Mendelson introduction to mathematical logic book for such course?

You are a life saver

Thanks for uploading this Antonio! I have really been enjoying these lectures so far.

I understand the topic Thunk You for this video

On the slide at 13:00, we add a new constant symbol c_phi for every phi. This is infinite constant symbols... but vocabulary must be finite right?

Im actually surprised by how low the number of subscribers and views are, this guy is really a good teacher

How do you know \aleph_0 \leq \kappa in the first place?

Does anyone have a reference for the formalisation of the proof of 2->3?

Can’t the axiom of choice be false. I mean its consequences are pretty unintuitive. And we do live in a discrete not continuous universe

Thinking Why V_omega is a set?

Thanks for the nice intro

Understand the symbols and settings now.

Syntactically implies

logically implies Satisfiable

The language for sentential logic is complete. Thank you, you are my math teacher of math. logic. I know that using "or" and "not" is enough but I don't know why. You explain it very well.

Now, learn the symbols tautologically implies and equivalence

Thank you, I get the idea and I think I can fill in the details later

Thanks you, that’s what I want to know❤

From Xotximilko’s comments From the course website on Math 125 Textbooks: Peter G. Hinman, Fundamentals of Mathematical Logic. Joe Mileti, Mathematical Logic for Mathematicians, Part I. Helbert B Enderton, A mathematical introduction to logic. And for 135 its Enderton's Set Theory .

12:46 To show that x < E(q) < y , we need to show that (i) x is a **proper** subset of E(q) and (ii) E(q) is a ** proper** subset of y. (ii) is true since q does not belong to E(q) while q belongs to y. However, for (i), I cannot understand why x is a **proper** subset of E(q).

A sentence is not defined in binary terms by its truth or falsity, it is defined solely by its coherence. Without coherence, or sense, there is no sentence. By "it" I mean a string of letters. If "satisfiable" and "not satisfiable" do not define a set of sentences, what makes sentences a "set"?

8:00 Why aren't we using s bar for the interpretation of the relation anymore?

Working through Modern Mathematical Logic by Mileti on my own. These lectures are a great complement

Thanks; I vaguely remembered this proof from my university class but that was years ago and I couldn't find my old notes. This really helped me remember it.

Thanks

Great work, very nicely explained!

why do you clap 🤔

17:10 If I wanted to use the subset axiom, could I say {{B} × B ∈ P(P(A) × A) : B≠∅} ?

Any detailed proof for the recursion theorem?

Thank you so much for sharing these lectures! Professor Montalban, which textbook do you recommend for the Math125 and Math135 materials? I cannot find it online, sadly.

Love it!!!!!!!!!!!

6:39 Why does eq change to supseteq?

Why can't a set belong to itself in the first place? Will such set lead to any contradictions?

Doesn't it make more sense to define field(R):=UU R, then we can prove that field(R)=dom(R) U ran(R)? Because otherwise it feels like circular reasoning (we prove field(R)=UU R without having a properly defined field(R)). Of course I'm not doubting the truth of the statement, just the logical progression

Saludos. Tal vez es el „equivalente" al 5⁰ postulado de Eucalides. Ya existe un agercamiento ynmodelo de planteamiento de un constructo geométrico que puede dar una otrra opción de "simplicidad" para una probable teoría de números, cercana a las cortaduras de Dedekind y coherente con Platón, Eudoxo y Charles Aanders Pierce. Due desarrollada desde fines del siglo pasasdo e inicios del presente, con avances en 2008-2010 y su fundamentación fuerte del 2019 a la fecha. Se basa, también como la Geometría de Hilbert, en Lineas y Puntos, siendo la linea "primero" que el punto y amplía el campo a la información y la memoria, elementos fundamentales de la Semiótica. Aborda los problemas derivados de los teoremas de Gödel, teniendo como uno de los fundamentos la Memoria como qualia o cualidad de un modo que implica una dualidad Memoria←→Información y, como en clases y conjuntos. Ojalá les interese iniciar un diálogo al respecto. Desde 2015 a la fecha, incluso una tesis de doctorado en españa comoarte algunos principios con lo postulado desde 2000-2001, y existe desde aprox. el 2015 una escuela en Alemania que usan, en un modelo similar más no equivalente, al modelo AHXIOM. Me encantará poder iniciar un diálogo al respecto. Gracias.

Amazing proof! Thank you very much :)

If you allow the universe to include transfinite levels of power set, then how could the axiom of regularity be possibly conceivable? By constructing V_omega you have built a set of infinite depth.

The Russel Paradox argument for the universe not being a set is unsound, since there are set theories avoiding such paradox. The valid way to prove it is through the power set cardinality argument.

Thank you.

What is the difference between “structure” “model” “interpretation” and “semantics” in first order logic and propositional logic?!

What is the difference between “structure” “model” “interpretation” and “semantics” in first order logic and propositional logic?!

What is the difference between “structure” “model” “interpretation” and “semantics” in first order logic and propositional logic?!

KIND SIR, WHAT IS THE difference between a “model” and an “interpretation” and “semantics”?

Defining for all using for all seems circular, same for exists...Wouldn't it be more precise to define them considering the formula a function of arity n, where n is the number of free vars, that goes to {true, false}, then for all is true if the function image is {true}... similar approach for exists...

How to prove that the assignment at the end to all the variables still satisfy every finite subset in gamma

Hey love your channel. May I ask a couple questions: Hey so here are the “soft” questions I have compiled. If anything is unclear just let me know! 1) Does naive set theory require attaching a logic to it to “work” or does logic require set theory to “work”? I am having trouble understanding the true nature of their relationship and they seem really connected during this first pass through some TH-cam videos. 2) With just naive set theory - no first order logic - can we make truth valuations? Can we even do anything at all in set theory without logic? 3) why is “first order logic” “fully axiomatizable”, but “independence-friendly first order logic” and “second order logic” isn’t? 4) Does this mean we can’t trust “independence-friendly first order set theory” and “second order logic” to always make true statements? If not, what consequences does it have if a logic isn’t fully axiomatizable? Thanks so much!

at 3:50 , on screen, how is “the set of all natural numbers below 10” equal to { x in N l x is prime } ?