Mathematical Logic, Lecture 1 (First-order logic: languages, structures and formulas)
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- čas přidán 26. 09. 2021
- These are video lectures for the Mathematical Logic course (Math 220A) taught by Artem Chernikov at UCLA in the Fall quarter of 2021.
In the first part of the course we will be following Chapters 2 and 3 of "A First Journey Through Logic" by Martin Hils and François Loeser:
bookstore.ams.org/stml-89
Followed by further material in model theory from David Marker's "Model Theory : An Introduction"
www.springer.com/gp/book/9780387987606
and my notes.
Thank you for the resources and great lectures. Your instruction is wholesome!
This is great. I've been looking for a high quality mathematical logic playlist on youtube and this seems to be it. Thank you Prof Chernikov.
Glad to hear that it's helpful!
Dear Prof Chernikov, thank you so very much for making your material available. This is VERY HELPFUL to independent learners and VERY MUCH APPRECIATED!!! Is it possible to have access to notes and hw?
These are awesome! are there some psets or referred textbook to accompany these lectures? I have been searching for a proper course on logic.
Is there any notes that are publicly available?
Is this Anton Petrov speaking?
c#acibo!
23:00
should logic symbols also include "for all" and "or"
We don't need to include those because they can be expressed using the existential quantifier, negation and conjunction - so we have chosen a minimal set of logical symbols that allows to express all the other ones, in order to keep the syntax as simple as possible.
Is the set of variables countable? If so, why?
It is. You can prove it by constructing the bijection f from N to the set of variables, defined as f(n) = v_n (greek letter ni pedex n).
Why did logicians decide that it is so? This I don't know yet. Probably because if we had infinite variables it would be impossible to write down most of them, and would be useless. Take for example the real numbers. We have access only to a small minority of them, the computable numbers. For the others we need an infinite string only to decribe one of them. The same would be for a set of variables with a cardinality more than countable. You'd need an infinite string to identify a generic variable, or an infinite amount of symbols (which is impossible to list and to describe).