All Questions
Tagged with philosophy set-theory
130
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Are quasi-sets (and therefore Schrödinger logic(s)) studied by mathematicians or are they purely in the domain of philosophers?
Context:
I'm a fan of different kinds of logic. I'm conflicted about whether different logics actually exist beyond, say, a philosophical oddity.
The Question:
Are quasi-sets (and therefore ...
- 45.7k
3
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136
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Which forcing technique implies "every set is countable from some perspective"? Which notion of "the same set" is used between models?
https://plato.stanford.edu/entries/paradox-skolem/ contains this claim:
Further, the multiverse conception leads naturally to the kinds of conclusions traditional Skolemites tended to favor. Let $a$ ...
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Are there any problems about the difference between set theoretic definitions of polynomials?
I am a novice about this question, so if there is a misunderstanding then I apologize for it.
As for Peano axioms, if I choose Zermelo natural numbers, and you choose von Neumann ones, then this doesn'...
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doesn't the independency phenomenon make a case for non-classical logic? [closed]
alright, this question is philosophical and somewhat fuzzy. i also admit to knowing little about logic. all in all, this question can possibly be easily resolved by either pointing to (perhaps even ...
- 495
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Finitists reject the Axiom of Infinity - are there groups who reject the others?
I've seen rejections of the Axiom of Infinity. This is called finitism. Some ultrafinitists even add the negation of the Axiom of Infinity. Definitely doable.
I've seen rejections of the Axiom of ...
- 351
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125
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What exactly makes the ordinals an indefinitely extensible concept?
I understand the principles of generation that cantor used to create the ordinals but I cannot see what exactly is the property that makes the ordinals an indefinitely open plurality and not the ...
- 21
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887
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Formally how do we view finite sets
This might be silly, but I have been thinking about how we would work with finite sets very formally.
So, $\{1,2,3,\cdots,n\} = \{k \in \mathbb{Z}^+ \mid k \leq n\}$ gives a representee for which any ...
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287
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Set theory and model theory: which set is ZFC?
I have yet another post about what is model theory doing and why is it valid; I hope I can be coherent.
(1) https://mathoverflow.net/questions/23060/set-theory-and-model-theory
(2) What exactly is the ...
- 19
1
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3
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652
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I don’t know what a natural number actually is
For some context I did a course on set theory where I was taught about ZFC, and the construction of the natural numbers, integers etc.
I think I was far too young to take the course because it’s left ...
- 480
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339
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What is the deal with the bizarre philosophy in historical and current axiomatic set theory? [closed]
Many respectable mathematicians have written about "true axioms" or similar concerns about whether all mathematical theorems are in fact "real" or "true". This seems to ...
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in modal set theory, why it is issue?
I have been studying the Iterative Set Concept within the context of the paper titled "Modal Set Theory" from Menzel specifically on pages 11-12.
"As we’ve just seen, the iterative ...
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319
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How should one understand the "universe of sets"?
One way to understand the axioms of $\mathsf{ZFC}$ is to see them as a describing the "universe of sets" $V$, together with the "true membership relation" $\in$. The universe $V$ ...
- 20.7k
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87
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Did Skolem (and others) consider all "legitimate" models to be "actually" countable?
In Thoralf Skolem's Remarks on Axiomatized Set Theory (van Heijenoort translation), Skolem says:
There is no contradiction at all if a set $M$ of the domain $B$ is nondenumerable in the sense of the ...
- 1,024
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66
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Criterion of Identity for 'set'
I'm looking for different criteria of identity for the notion of 'set'. I know that the standard criterion of identity is extensionality but I was wondering if there are others. I looked around but ...
- 19
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Concerns with Global Choice vs Ordinary Choice
I know that the axiom of choice is widely accepted by mathematicians nowadays, despite early worries about it. What is the sociological status of the axiom of global choice these days? And are there ...
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