Notes May 7

Ack.  I don't think I ever posted this.  It's probably too late to help anyone in the class, but maybe it'll help posterity.

The PDF:
https://docs.google.com/open?id=0Bywlg79R0_RDN1JtVjRjaVhFNG8


TeX:
https://docs.google.com/open?id=0Bywlg79R0_RDY1NKOFJLOWVVRzQ

    As you should have heard already, my plane flight was cancelled (due to a "missing first officer") and they could not reschedule me back in time for class Friday.  So class is cancelled this Friday, but we will meet as planned on Monday.

    My apologies for the disruption.

    Sam

Scribe notes for May 4 -- bounded quantifiers

Here are the scribe notes for May 4 on bounded quantifiers: pdf and tex.

Scribe Notes for Friday, May 18

The pdf and the tex files.

Notes for Wednesday, 5/16/12

the pdf is here and the tex is here

Notes for May 14

The pdf and the tex files.

Notes are posted for Part II of Friday's lecture (May 11).   If you notice any typos or other errors, corrections are appreciated.

The PDF file is here.  The source file is here.

Sam

Scribe Notes for Friday, May 11

Here are the scribe notes for May 11 (on \(\Sigma_1\)-defined functions and some more bootstrapping): pdf and tex.

notes for may 9th

the pdf is here and the tex is here

Scribe notes for April 27th

Scribe notes for April 27th: PDF and TEX.

-James

Scribe Notes from May 2nd:
PDF LaTeX

Scribe Notes for April 30

Here is the tex and here is the pdf. If I made any errors let me know and I will update the document.

April 25

Notes are here.

Scribe Notes for April 23

Here is the tex and here is the pdf.

Scribe notes for April 20

Here are the scribe notes for April 20th: PDF, TeX
The topic: Primitive recursion -- sequence coding and Turing Machines

Scribe Notes: Wednesday, April 18th

Here is the PDF.
If I made any errors let me know and I will update the document.

Notes April 13

Notes are here.

Scribe notes from April 6th

Here is the pdf, and here is the tex.

Scribe notes from 4/16

Here is the tex and pdf.

Scribe notes from Mar 16, 2012

Here is the pdf. And here is the TeX.

Halting Problem in Iambic Tetrameter

Since we just saw a proof of  the undecidability of the halting problem, I thought I'd share with everyone my favorite version of the proof: Scooping the Loop Snooper

Scribe Notes from Wednesday, April 11

Here is the pdf. And here is the TeX.

For anyone who wants an example of a quine, check out this one (it's a python script).

Scribe Notes from Monday, April 9

Here is the pdf. And here is the TeX.

Class Notes

Here is the pdf and the tex files for the notes from April 2nd and 4th on Turing machines.

Turing's paper "On computable numbers, with an application to the Entscheidungsproblem" is freely available here, although in somewhat hard-to-use form.

scribed notes

TeX

pdf

My office hours for finals week:

Monday 4:00pm,  Tuesday 2:00pm (Priority to Math 155A)
Tuesday 5:00pm, Wednesday at 5:00pm (Priority to our class).

Sam

Homework Question

So I'm not sure how often people look at the blog, but this seems a good a place as any.

For question 6, part a, is there something we are supposed to prove?  It looks to me like a definition required for b-e, but I don't see a question for part a.

Also, while I'm here, is there still a take home final?  Or is this last homework sorta the final or something.

Notes for Wed. March 14

Here are the notes and here is the TeX.

Lecture notes for March 5, 2012

PDF TeX

The Notes Thus Far...

I just combined all the pdf files for any currently posted scribe notes, so that I wouldn't have to keep flipping through all the different files one by one. If anyone is interested, I've posted the file here.

Scribe Notes for March 7th
PDF TeX

Scribe Notes - March 2nd, 2012

PDF TeX

Notes for Feb 27

Here are the notes for Feb 27, which cover the Lowenheim-Skolem Theorems and the Los-Vaught test.

pdf and tex

Matt

Notes for Wed. February 29

Due to an aberration in the spacetime metric brought on by the fact that today is February 29, the notes from today are being posted before the notes from Monday.  Here are the notes and here is the TeX.

Includes:

• An application of the Łoś-Vaught test
• A taste of computability
• Skolem's Paradox
• An introduction to the completeness theorem for uncountable languages.

Notes for Feb 24

Here are the notes and tex file for February 24. If you see any errors, omissions, or improvements let me know.

Scribe Notes for February 22

Here is the pdf and here is the tex file. Enjoy!

Scribe notes from February 17, 2012

Hi all,

Here are the scribe notes from Feb 17, 2012. (TeX code is available here.) In class, two notations for \( \mathcal{M} \) were given: one without tilde and the other with tilde. The tilde notation works well for simple symbols such as \( \tilde{b} \), \( \tilde{c} \), and \( \tilde{t} \). But, I think, it is not for long terms such as  \( \widetilde{f(t_{1},\ldots,t_{k})} \)   (\widetilde{f(t_{1},\ldots,t_{k})}) . 

Have a great weekend!

Best regards,
Tomoya Sato

Scribe notes from February 15, 2012

Here is the pdf, and here is the TeX.

Notes: Monday, Feb 13

The PDF is here. The TEX is here.

Scribe notes from Feb 10, 2012

Here are the scribe notes from Feb 10, 2012. (TeX code is available here.) They introduce Frege-style systems for first order logic (aka Hilbert-style systems), as well as sequent calculus systems for first order logic (both LK and LK_e systems).

Bob Chen emailed to ask "What is a resolution derivation? We couldn't find the term in the 'Handbook of proof theory' (there it only mentions resolution refutations)."


My answer:  A resolution derivation is the same as a resolution refutation, except not requiring the final clause to be the empty clause.   In particular, if there is a resolution refutation of a clause \(C\) from  a set of clauses \(\Gamma\), then \(\Gamma \vDash C\) holds.   (We proved this fact in class as part of proving the soundness of resolution.)


Sam

Announcement: Homework II is now due on Friday, February 10.

For Math 260 students (UCSD, Winter-Spring 2012).

This blog is intended for discussions accompanying the Introduction to Mathematical Logic course, during Winter and Spring 2012.  

It will be set up so students can create new posts, and anyone can view or answer them.  For this, if you are attending the course, please send me your preferred email for blog posting.  It is probably best if you have a gmail address, but I expect it will work also if you do not have a gmail address.    

Any discussions related to the course is fine, including discussions about, and hints for, homework problems.

It is a bit counter-intuitive how to use Blogger: To view a particular post including all of its comments, you must either click on the post title in the sidebar on the right side of the screen, or on the "Comments" link at the bottom of the past.

You can use LaTeX commands in either posts or comments, which are implemented with MathJax and should work in almost all up-to-date browsers.  Note that enclosing math in single $'s does not work.  However, you may use "\(\backslash(\)" and "\(\backslash)\)" for inline math and double dollar signs or "\(\backslash[\)" and "\(\backslash]\)" for displayed math.  Examples:  $(y+\sqrt z)^{-1}$ and  \( \sin^2 x^2 \).  And, a displayed equation is: $$\frac 2 3$$
Another displayed equation is here:
\[
\forall x \exists y (x\le y \land y\le x \leftrightarrow x=y) .
\]

Sam Buss
sbuss@math.ucsd.edu
sambuss@gmail.com