Unanswered Questions
52 questions with no upvoted or accepted answers
4
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Is there a counterpart semantics available for the multiverse standpoint in set theory?
I've been working on something that might be usefully denoted "the Dual Continuum Hypothesis," which is based on the following from Asaf Karagila on the Math Stack Exchange:
We know that ...
- 2,637
4
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Are Quine atoms counterexamples to the irreflexivity of grounding?
It seems commonplace enough in the literature on grounding to find the claim that x grounds {x}. It is also a commonplace that grounding is irreflexive. But what about a Quine atom, then? For this is ...
CommunityBot
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3
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In set theory: What is the motivation for transitioning from first-order language to plural logic language?
I am reading Burgess's paper titled "Plural Logic and Set Theory." In this work, the motivation for transitioning the language of set theory from first-order logic to plural logic is based ...
- 50.2k
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For "⊰" = "grounds" and {C, D} = {~A, ~B}, does (C | D) ⊰ ~(~A ∧ ~B) ⊰ (A ∨ B)?
One paradigmatic example of grounding is supposed to be that of conjunctions-in-their-conjuncts and disjunctions-in-their-disjuncts. But per the duality of classical conjunction and disjunction, and ...
CommunityBot
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2
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Would "to avoid the class/set distinction" be, or not be, an ad hoc reason to propose a couniversal set?
Once upon a time, von Neumann proposed the axiom of limitation-of-size, which says that any class "too large to be a set" is then a "proper class," meaning that there is a ...
CommunityBot
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2
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Is there a difference between "is an intensional element of" and "is an extensional element of"?
There is a version of set theory according to which there are two flavors (types? categories?) of elementhood relation, and if it's ultimately coherent, it does offer a solution to Russell's paradox (...
CommunityBot
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Could the axiom of infinity be in itself inconsistent?
I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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Does Reflective Set Theory "RfST" fulfill the requirements of founding Category Theory and Mathematics?
On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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How does Badiou analyze natural situations?
I'm having trouble applying Badiou's method of looking at situations as sets (EDIT: specifically sets in a model of ZFC). The following example was in the introduction to one of his books, Infinite ...
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Using paraconsistent logic, can we construct a conceptually stable set theory where proper classes both are and are not sets?
Suppose that the superclass problem is the problem of defining a new infinite hierarchy of set-like concepts over the concept of proper classes. For example, some superclass types in the literature ...
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Does the question of grounding affect approaches to Benacerraf's identification problem?
We will be referring to metaphysical grounding, of which the grounding of a singleton in its element is often held forth as a paradigmatic case. To mark out such a relation, we will use the fancy less-...
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how to solve Russell's paradox in modal set theory?
I am currently reading Nil Barton's "Iterative Set Theory." at pp.42-45.
It explains that modal set theory resolves Russell's paradox, but I don't fully understand it.
If a set x satisfies ...
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1
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Why is this argument valid?
I m reading Linnet's paper 'pluralities and set' where his claim said that collapse principle lead contradiction if we didn't assume 'it is possible to quantify over absolutely everything'
He uses ...
- 50.2k
1
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What papers or books should I read in order?
I have been reading literature on modal set theory and am currently reading Putnam's "Mathematics Without Foundations," which is known for being one of the earliest presentations of this ...
- 499
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Can a set be uncountable in one sense and countable in another sense?
Can a set be uncountable in one sense and countable in another sense? Or in other words are there senses in which the set of all real numbers satisfies the Peano Axioms? I ask because of the following,...
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