Questions tagged [set-theory]

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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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Forcing and Philosophy

The only (ontological) connection between Forcing (Cohen) and Philosophy i know is the work of Alain Badiou. Are there any other philosophers who have worked on this topic?
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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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The empty set as an atomic unit

I was reading some perspectives on the empty set in ZFC set theory. To my understanding, every other set that we can explicitly show to exist is made up of the empty set and sets of the empty set. ...
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Are there versions of set theory in which a concrete object, say an apple, can be a member of a set

Certainly, when we apply set theory, we consider collections of concrete objects as sets. For example, when I count 5 apples, I establish a bijection between the number 5 ( which is defined as the ...
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82 views

Are the foundations of mathematics “doomed” to be set-theoretic in nature?

Let's say we want to come up with a foundational theory for all of mathematics and let's say that it is embedded in first-order logic. Note that the machinery of first-order logic is described with ...
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99 views

Is it 'natural' to hold that big sets and proper classes exist?

Various set\class theories present different kinds of ontology, broadly speaking there is the dichotomy of classes versus Ur-elements, and the former can be further subdivided into sets and proper ...
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List of topics in philosophy relevant to mathematics, and open problems in them?

I know of open problems in model theory, but would like to know about philosophical problems (philosophy of language, Husserl's phenomenology ) that have relevance in set theory or type theory.
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497 views

Theology of set theory

Absolute space and time are said to emanate from Aristotle. The Church acted as custodian of these concepts from early on up to recent times. I am thinking about another issue, namely that of ...
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Analogy of Set and Subset and Contracts in abstracto and Marriage in concreto/in particular

I had a talk with a professor of family law and we are frequently told that there are general ordinances for contracts in general and particular ordinances for marriage. I am problematised by the ...
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How much this theory fulfills of criteria for a foundational theory of mathematics?

[EDIT] The criteria for a founding theory of mathematics, especially if it uses large cardinal axioms that I want to refer to are those of Harvey Friedman's 2000 criteria given in pages 5-6 of the ...