/r/modeltheory

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Discussing model theory

/r/modeltheory

77 Subscribers

4

Does anyone want to take over this sub?

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.

1 Comment
2024/02/14
17:04 UTC

1

What exactly does Numerical insegregability means ?

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...

0 Comments
2024/02/13
06:55 UTC

2

Minimal non-standard number in non-standard models of PA

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 ?

12 Comments
2024/02/12
17:58 UTC

2

Join r/MathematicalLogic!

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!

0 Comments
2019/03/04
03:17 UTC

2

Anyone there?

So I see this subreddit has been dead for quite a bit, anybody still willing to start getting this sub active again?

2 Comments
2019/02/22
08:05 UTC

3

Looking for a comprehensive History of Model Theory source. Any recommendations?

I have a mathematics, logic, and philosophy background. Just wondering if anyone knows of a nice history that I may be unaware of. Thanks!

2 Comments
2015/03/21
06:06 UTC

1

You get to recommend 1 model theory text. Which is it and why?

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!

3 Comments
2014/02/24
17:31 UTC

2

Introduce yourself: Who are you and what is your affinity to model theory?

Is it a hobby, a tangent, or your career?

Do you have any cool research to tell about?

Share with us :)

2 Comments
2014/01/26
15:39 UTC

1

Hi, welcome to model theory

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.

7 Comments
2014/01/25
18:47 UTC

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