/r/modeltheory
Discussing model theory
/r/modeltheory
I created it during my M.Sc years ago, and have since shifted my interest many times and frankly, have lost all touch with model theory.
I think it would be for the best if someone who cares about the field inherits it.
Quine said that 1st order theories of PA are Numerically insegregable , i.e. it can't distinguish between standard and non-standard numbers, refer this - https://en.wikipedia.org/wiki/Ω-consistent_theory#Definition ( last line in the 2nd paragraph of the linked subsection ' Definition ' in the page )
I want to ask how exactly is the theory isn't able to distinguish ? Does this means that we cannot write a predicate in 1st order PA which accepts or is true only for standard natural numbers ? If that is so than atleast I think that we can definitely write such predicates, we can just define a predicate which takes a number iff it has a predecessor, since non-standard numbers don't have a standard predecessor so this predicate will only accept standard numbers... Is this correct, or maybe Numerical Inseggregability is something else... Please help me...
Excuse me, if the question sounds too naive.
From godel's incompleteness theorem we know that there would be non-standard models where the godel sentence would be false. These models will have an initial segment isomorphic to standard natural numbers. Will there be a minimal non-standard number in such models such that every number smaller than it is a standard natural number and every number bigger than it would be non-standard ?
Since non-standard model would be a model of arithmetic then i think there should be a minimal non-standard number, but then maybe my concept is unclear about it. Any help ?
Hey guys, I just started a subreddit, r/MathematicalLogic, for mathematical logic in general (i.e model theory, set theory, proof theory, computability theory). I hope you guys join so we can get people who are interested in logic in one subreddit, even if it's just a few!
So I see this subreddit has been dead for quite a bit, anybody still willing to start getting this sub active again?
I have a mathematics, logic, and philosophy background. Just wondering if anyone knows of a nice history that I may be unaware of. Thanks!
I will be doing a directed reading on model theory next semester and I can nominate the text I would like to work from. I have read such positive things about little Hodges, but before I commit myself and my money, I would like to hear everyone's suggestions. It is supposed to be a concise introduction designed to get the newcomer up to speed with fundamental results.
To give a sense of where I am, so to speak: I am "logically mature," have a decent knowledge of set theory, but will probably have to supplement whatever text I choose with an abstract algebra text (recommendations for one are welcome as well!).
Thanks for your input!
Is it a hobby, a tangent, or your career?
Do you have any cool research to tell about?
Share with us :)
Not a lot to say.
It just seems that mathematical logic is becoming too broad to find people who share your interest. In particular, it would be nice to have a place to discuss the ever growing niche of model theory and share resources and ideas.
Please don't tap on the class.