Відео

🔥🔥🔥

phd studentin von Dir? :D

this channel is a real gem

Probably my favorite video on youtube, big fan

Bring back those videos. We need more formal videos on foundations of knowlegde

Love it!!!!!!

Microseconds be like: 15 15 15 60 Microseconds later: 23 10⁶ 10^10^100 TREE(3) Omega

Thanks, what source do you recommend?

Bouldering during lockdown is also NP hard😹

By model, do you mean group, ring, etc.?

Wow! I got lost early in the video due to the jargon. I understand isomorphisms, but I did not comprehend the other definitions. I will need to think about the statement "clearly the two structures are not isomorphic".

Super interesting video and really understandable, even for me as a set theory beginner. Thank you for sharing!

Just started watching this lecture series. Thanks for making it open to the public. If it is not too personal I'd like to ask if you are a dj since it seems that way judging by your profil picture. It would be interesting because not many mathematicians I know have this hobby

Great video! You briefly talked about categoricity, I think you should make a video on categoricity transference (specifically in infinitary logics) and abstract elementary classes.

Ich finde es so schade, dass nicht alle Profs ihre Videos so gestalten. Vor allem bei der Mathematik. Also da hat Prof. Bodirsky einen sehr guten Weg gefunden, um das Interesse der Studenten zu wecken.

Manuel Bodirsky ist einer der besten Profs an TUD. Ganz ehrlich, wer wünscht sich nicht so einen Prof?

Ich glaube bei 0:06 hast du dich verschrieben. Ich glaube ich bin aber auch der einzige, der sich diese Aussagen angesehen hat. XD

I quickly ceased to understand, but I certainly appreciate this video.

great videos!!!

I have the book Model Theory by Cheng and I'm trying to work through it. It's quite dense. The first chapter talks about semantics, syntax, and theories. Maybe you can explain why these distinctions are made as it seems to me to all be the same(and which it is since he proves they are the same). It seems to me that the distinctions add unnecessary complexity through obfuscation rather than serving any actual theoretical purpose. At best all I can come up with is that historically semantics, theories, and syntax were thought of differently because the theories connecting them were not well developed. When I learned logic it was more from the syntactical approach and that is typically how I break things down. About all I have gotten out of the distinctions is that there are typically 3 approaches to think about propositional logic which as only helped me in realizing why some forms of thinking seem "off" to me... and it is because they are semantic approaches. Other than that I can't seem to reconcile why one should go to the trouble of making the distinction, maybe you have some good reason why it is done? I haven't worked through model theory much but I've always had in the back of my head that there was far more to theories and Chengs book seems to make it explicit(and I guess that is what model theory is all about). But it seems overly formalized in a way that feels very pedantic without real purpose(I haven't worked though the book yet though so I'm hoping there is more to it). I do have an extensive background in logic but more from a mathematicians point of view and along the lines of simply learning mathematical theories, category theory, basic logic courses, computation/computer science, etc. I always feel a little uneasy in when logicians present their material. I've seen the same thing but the way they go about it always feels like they haven't learned abstract syntax tree's, category theory, and the like(obviously they know something about it but the language jargon seems to be geared towards something else). Of course maybe the point is not to be circular but pretty much all life is circular in some sense. For example, Models are defined as simply a subset of a language of sentence symbols. Then one makes a relation between models and "truth tables" by assigning values. What's the point? It's it solely for language? I grew up with truth tables and I automatically translate models in to truth labels. It seems perfectly natural to do this... but if there is a distinction being made it makes me think I'm doing it wrong. It really makes no sense to me to say something is "true in a model" and "true in a truth table" as different statements(but only the 2nd is natural to me). Now if I assume historically it wasn't know they were equivalent then fine, I get it but I then rather learn model theory that doesn't make the historical distinction since it's much more work to track the unnecessary differences while trying to learn the technicalities of model theory. (learning something should be as easy as possible, not unnecessarily complicated)

Hey professor -- if you could include definitions in future videos, I think it would make these videos more usable for self-study :) So a relational structure \( C = (c, \{ \gamma_i : i \in I \} ) \) is a set \( c \) and set of relations \( \{ \gamma_i : i \in I \} \) on \( c \), and a substructure \( D = (d, \{ \delta_j : j \in J \} ) \) is just a subset \( d \subseteq c \) and set of relations \( \{ \delta_j : j \in J \} \subseteq \{ \gamma_i : i \in I \} \) on \( d \) ? When I embed \( A \) into \( C \), I inject \( a \overset{f}{\hookrightarrow} c \) such that \( \{ f(\alpha_k) : k \in K \} \subseteq \{ \gamma_i : i \in I \} \) ?

Thank you for video!

Zermelo-Frenkel deez nuts

hi

hi

muy bien

Tres Good!

It is amazing how such hidden gems as this lecture shed light to platonic dialogues such as Cratylous and Parmenides and Republic and Timaeus and Theaitetus.

This is the most interesting way to teach someone about the TCSPs.. LOL

You should make clear why a (von Neumann) ordinal needs to be a transitive set (the fact that it should be well ordered (by the unique given relation in ZFC, the membership) is more clear, at least to me). Or simply claim first that all we need are well ordered sets (but there it comes the axiom of choice) and then add a unique well defined set (that is, an ordinal) order isomorphic to that well ordered set

Ich nehme gern eine Allmenge an, die ich definiere als jene Menge, die beliebige Elemente umfasst *und* die konsistent ist. Das ist für mich die eigentliche Allmenge bzw. „die ganze Welt“, denn ich möchte schon auf „das Ganze“ referieren oder darüber nachdenken können, ohne mich in Widersprüche zu verstricken, wie bei der Annahme von Russell‘s Allmenge. Könnte man das in ZFC so definieren o. ist ZFC mit FOL dafür zu ausdrucksarm?

Wenn man also das 9. Axiom wegnimmt, dann ist folgende selbstbezügliche Menge möglich: a = {a}? Wenn zB eine Menge M die Mengen a, b einschließt, dann gilt: M = a gdw. a = {a, b}? Damit könnte man nämlich M „von innen heraus“ vollständig beschreiben.

very interesting

Amazing! Thank you very much

Also, another question: in the proof, A and B are finite. What happens when it is not the case..?

I am sorry, but what is HSP^fin of B??

thank you so much, this is very helpful

At 12:24 did you mean the logical AND instead of the logical OR?

Fantastically clear, especially for someone not particularly versed in logic! thanks

Amazing video!

Very great video, thank you

Hello, professor. I came across your channel when I was searching for ways to understand concepts in logic, and I was very intrigued by the concepts that are introduced through your videos. I'm an undergraduate maths student, and I'm only studying through my second term, yet I do wish to study more advanced subjects. I was wondering if you could possibly introduce textbook resources for understanding and having an introduction to the subject of your videos and your field? Thank you very much.

Hi, lädst Du die ganze Serie hier hoch? Würde mich freuen!

All you need is maths 💙

Ach das TBA hat wieder offen.

(Hopefully correct) Solution to the exercise at 5:08 : This is the classical „show all items with this property must lie in the closure, and that all these items already form a closed subset“-type situation. In the examination below I consider a „substructure“ to be given just by the base set and not the tuple (set, functions, relations), since the latter two are uniquely determined by A. It is easy to see that a subset can carry a substructure if and only if it is closed under function application on any tuple of elements. Let SS: P(B) → P(B) be the „substructure generated by“-Operation, which is of course monotone, extensive, and idempotent. Let further A := {t^\underline{B} (g1, …, gn) | gi \in G, t τ-term in n variables} as constructed. Note first that A actually extends G, since the term t(x_1) = x_1 is as a term function nothing but the identity, so every g in G is representable as t^\underline{A}(g). Furthermore, a simple inductionwe over the term-depth (the unique amount of steps we have to apply the inductive definition of a term to obtain a term t) shows that any substructure must be closed under the operation t^\underline{A} for any term t - roughly, because substructures have to be closed under function evaluation, and terms are just functions stacked in functions. In particular, if C is any substructure containing G, then C must contain A. Hence, A ⊂ SS(G) = \bigcup_{C substr. cont. G} C. On the other hand, A clearly is closed under all the functions, so it is a substructure. In terms of our closure operator, SS(A) = A. Combining the two, we get G ⊂ A, which by monotonicity becomes SS(G) ⊂ SS(A) = A , but A⊂ SS(G) as per the first observation. Hence, SS(G) = A, yielding the desired characterization.

Am I correct in observing that the correspondence (substructures ⇔ subsets whose injection is a homomorphism), which we know from universal algebra, fails to hold due to the differing demands on relations? For instance, the inclusion of a weak subgraph H≤G does preserve the “truth” of the relation, making it a homomorphism, but not its “falsity”, implying that H fails to be a substructure.

Tischbouldern mit Querverstrebungen, an denen man sich abstützen kann, ist aber doch schummeln ;)

Es waere schoen, wenn die Sprache nicht komplett auf dem linken Kanal liegen wuerde, sondern im Stereomix zentriert waere - mit Kopfhoerern ist das sonst recht anstrengend zuzuhoeren.

Aber wie lange müssen die Kastanien in den Ofen? Und bei wieviel Grad?