All Questions
Tagged with model-theory soft-question
65
questions
4
votes
1
answer
140
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(When) are recursive "definitions" definitions?
This is a "soft" question, but I'm greatly interested in canvassing opinions on it. I don't know whether there is anything like a consensus on the answer. Under what conditions (if any) are ...
- 95
2
votes
0
answers
83
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Comparing mathematical objects by the "rigidity" of their definitions
A loose interest of mine recently has been ordering mathematical objects by how "combinatorial" their study is, in broad terms.
I consider the study of a mathematical object more “...
- 497
1
vote
1
answer
68
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(soft question) I'm giving a talk on model theory to undergrads in a few weeks, thoughts topics to include/exclude
I am an undergrad and have been doing independent study on model theory for 6+ months now, and am slated to give a talk to undergrads later this month on model theory. I aim to give a soft ...
- 104
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0
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84
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What is the significance of the difference between I$\Sigma_3$, I$\Sigma_{30}$ and I$\Sigma_{3000000}$ and $PA$?
There is of course a difference for logicians, but from a non-logician-mathematician's perspective, what is the real significance of arbitrarily complex induction predicates?
Are there perhaps ...
- 684
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145
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Seeking Suggestions for PhD Topics in Model Theory, Focused on Combinatorics in NIP Theories and Tameness
Hello Math Stack Exchange Community,
As I embark on the journey of selecting a PhD research topic in mathematics, my interests are gravitating towards model theory, with a specific focus on ...
- 159
3
votes
1
answer
180
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Treatment of mathematical logic with less bookkeeping? [closed]
My only real experience with mathematical logic is an undergrad-level model theory class that I took some years ago. My (perhaps fair, perhaps unfair) take away from this class was that mathematical ...
- 777
1
vote
1
answer
91
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Resources for "Bell Machover"
Recently, I've been reading through A Course In Mathematical Logic by John Bell and Moshé Machover. However, it's not always the easiest book to understand. What might be some good supplements to have ...
- 183
5
votes
3
answers
215
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Examples of classes of structures which are "surprisingly" axiomatizable.
This is a bit of a soft question, but I am interested in a list of classes of structures (in the sense of model theory) which are "surprisingly" first-order axiomatizable classes. Meaning, ...
- 21.5k
5
votes
0
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110
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Examples of Substructures that "do not know they are that substructure"
Just learned $\mathbb{L}\vDash \mathbb{V}=\mathbb{L}$ and was warned that this property is not obvious with the counterexample mentioned being $HOD$. I can think of a few examples of definable ...
- 1,926
4
votes
1
answer
197
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Applications of Keisler measures
Keisler measures are finitely additive measures on the Boolean algebra of the definable subsets of some model.
They were introduced by Keisler in 1987 and did not receive much attention until ...
- 85
1
vote
1
answer
173
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How different are types in the single-sorted case of first-order logic vs the many-sorted case?
How different are types in the single-sorted case of first-order logic vs the many-sorted case?
Marker's Model Theory: An Introduction, which I'm reading, uses a single sort for FOL (or, perhaps more ...
- 11.9k
0
votes
1
answer
60
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Proper collections in ZFC
Consider a fixed model $M$ of ZFC or ZF.
A "set" $s$ in $M$ is a single element of $M$'s universe. One can identify a
collection of sets (i.e. collection of elements of $M$'s universe, as ...
- 109
1
vote
0
answers
27
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Name for simultaneous mapping from one structure+wff pair to another
Is there a name for a kind of map that simultaneously transforms structures and wffs?
The motivation for this kind of map is the existence of various systems like free logic and plural logic. It's ...
- 11.9k
1
vote
0
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52
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Conventions for distinguishing the two senses of an ultrafilter on X
Are there any well-established conventions to distinguish the two senses of being an ultrafilter on a set $X$ (when $X$ happens to be equipped with an ordering)?
This ambiguity is confusing at first; ...
- 11.9k
2
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0
answers
103
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Books/Resources for studying Number Theory as a First Order Theory and Model Theory
I just finished reading the completeness and compactness proofs of FOL and was wondering if there were any resources/books to study Number Theory as a First Order Theory. Can anyone provide me some ...
