I’m primarily interested in number theory, but I have a great deal of interest in analysis generally (more pure analytic things than anything numerical), which originally developed since it arises from set theory quite directly. I regret that I have never had direct access to a working logician.
I wouldn’t say that I have a research area yet, but I expect it will be in either algebraic number theory or PDE. I guess I’m in a rather small group of people who can say that with a straight face, since they’re on opposite ends of the spectrum.
Coincidentally I am in the process of writing my final advanced logic assignment as we speak (I wouldn’t call myself a working logician as a) I’m undergrad, and b) rarely working). My module focuses on the lead up to Godels incompleteness theorem, so overlaps with set theory related stuff a lot. I might be able to answer some general questions but no guarantees.
Know how you feel about doing very different things simultaneously, done both political philosophy and logic recently, odd shift of gears.
Random question You wouldn’t know how to show the rand of an increasing total recursive function is a recursive set would you? Or why if a theory has a arbitrarily large finite model it has an infinite model?
Odd thing about doing high level stuff is realising that the infrastructure you get used to doing lower level stuff (wikipedia articles, decent textbooks, etc.) ceases to exist. I feel increased sympathy for people pre information age.
You’d have to explain what the rand function is, since that is apparently an un-Google-able term unless you want Ayn Rand (I don’t), the C++ random return function, or something called the RAND corporation.
I’m the kind of person who reads things like Fixing Frege for fun after prelims are over.
Edit: Oh, & I don’t mean to be rude, but I probably wouldn’t call anyone a working mathematician/logician unless they were actively doing research either in a post-doc/tenure position or in industry (eg at Microsoft).
You’d have to explain what the rand function is, since that is apparently an un-Google-able term unless you want Ayn Rand (I don’t),
Ah sorry meant “range” not “rand,” nevermind think I got it. [I apologise for shamelessly pumping you for question answers.] As for Ayn, no-one does.
Would you recommend “Fixing Frege?” Think I’ve read bits and pieces of Burgess before but it never made a massive impact.
I’d agree with you on the definition of working logician, the post docs and lecturers I’ve worked with are on a completely different level from even the smartest student. Not quite thousand year old vampire level but the same level of difference as a native language speaker and a learner.
It helps that generally (ie unless you’re at Princeton/Cambridge/etc) the faculty at a given school will have come from much stronger schools than the grad students there, and similarly for undergrads/grads. And by “helps” I mean that it helps maintain the effect while explaining it, not that it helps the students any.
As far as the range of a recursive function goes, isn’t that the very definition of a recursive set?
I’m definitely enjoying Fixing Frege. This is the third Burgess book I’ve read (Computability & Logic and Philosophical Logic being the other two), and when it’s just him doing the writing, he’s definitely one of the clearest expositors of logic I’ve ever read.
Apparently, he also gets chalk all over his shirt when he lectures, but I’ve never seen this first-hand.
I’m primarily interested in number theory, but I have a great deal of interest in analysis generally (more pure analytic things than anything numerical), which originally developed since it arises from set theory quite directly. I regret that I have never had direct access to a working logician.
I wouldn’t say that I have a research area yet, but I expect it will be in either algebraic number theory or PDE. I guess I’m in a rather small group of people who can say that with a straight face, since they’re on opposite ends of the spectrum.
Coincidentally I am in the process of writing my final advanced logic assignment as we speak (I wouldn’t call myself a working logician as a) I’m undergrad, and b) rarely working). My module focuses on the lead up to Godels incompleteness theorem, so overlaps with set theory related stuff a lot. I might be able to answer some general questions but no guarantees.
Know how you feel about doing very different things simultaneously, done both political philosophy and logic recently, odd shift of gears.
Random question You wouldn’t know how to show the rand of an increasing total recursive function is a recursive set would you? Or why if a theory has a arbitrarily large finite model it has an infinite model?
Odd thing about doing high level stuff is realising that the infrastructure you get used to doing lower level stuff (wikipedia articles, decent textbooks, etc.) ceases to exist. I feel increased sympathy for people pre information age.
You’d have to explain what the rand function is, since that is apparently an un-Google-able term unless you want Ayn Rand (I don’t), the C++ random return function, or something called the RAND corporation.
The second question is due to compactness.
I’m the kind of person who reads things like Fixing Frege for fun after prelims are over.
Edit: Oh, & I don’t mean to be rude, but I probably wouldn’t call anyone a working mathematician/logician unless they were actively doing research either in a post-doc/tenure position or in industry (eg at Microsoft).
Ah sorry meant “range” not “rand,” nevermind think I got it. [I apologise for shamelessly pumping you for question answers.] As for Ayn, no-one does.
Would you recommend “Fixing Frege?” Think I’ve read bits and pieces of Burgess before but it never made a massive impact.
I’d agree with you on the definition of working logician, the post docs and lecturers I’ve worked with are on a completely different level from even the smartest student. Not quite thousand year old vampire level but the same level of difference as a native language speaker and a learner.
It helps that generally (ie unless you’re at Princeton/Cambridge/etc) the faculty at a given school will have come from much stronger schools than the grad students there, and similarly for undergrads/grads. And by “helps” I mean that it helps maintain the effect while explaining it, not that it helps the students any.
As far as the range of a recursive function goes, isn’t that the very definition of a recursive set?
I’m definitely enjoying Fixing Frege. This is the third Burgess book I’ve read (Computability & Logic and Philosophical Logic being the other two), and when it’s just him doing the writing, he’s definitely one of the clearest expositors of logic I’ve ever read.
Apparently, he also gets chalk all over his shirt when he lectures, but I’ve never seen this first-hand.