Tagged Questions

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Transfert principle of a conservative extension of ZFC

In the following paper, there is a theory called $^*ZFC$ in the language $(^*,\in)$. The *-map is (more or less) defined on the Von Neuman hierarchy $S$ and verifies the following axiom schemata true ...
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Is maths = set theory + logic? [on hold]

It seems to me that most branches of mathematics are just an application of set theory and the rules of logic. You just definite particular types of sets and study their properties. For example, in ...
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Founding Arithmetic on geometry

In the past I found some fleeting references that some (Frege in his later years being one of them) tried to found arithmetic not on set-theory and logic but on geometry and logic. Unfortunedly Frege ...
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Are there ordinals other than the set of natural numbers which satisfy this property?

Let $\alpha$ be an ordinal. We say that $\alpha$ is good iff for every $\beta\in \alpha$, there exists $\gamma\in \alpha$ such that $|\scr{P}(\beta)|\leq |\gamma|$. Question: Is the set of natural ...
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A Question Regarding Forcing in Gödel's Constructible Universe in Infinitary Logics

In his answer to the MathOverflow question Gödel's Constructible Universe in Infinitary Logics, Prof. Hamkins gives a very interesting answer and proof to user46667's second question: (2) What is ...
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Are there classes with different sizes?

Are there classes with different sizes ? I will put a precise statement of my question below: Are there two well formed formulas $P,Q$ each with one free variable such that there is no well formed ...
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Skolem Hulls in $H_{\omega_2}$

Consider a model of the form $\mathfrak{A} = (H_{\omega_2}, \epsilon, \prec, f_0, f_1, ...)$, some expansion of $H_{\omega_2}$ in a countable language, with $\prec$ giving a well-order. Does there ...
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What is the relation between axiomatic set theory and logical quantifiers?

On the one hand, the logical predicates $\forall$ and $\exists$ are defined using the concept of a Domain of Discourse, which itself is defined as a set (at least according to wikipedia). On the ...
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On Counted Languages

In my recent question on Godel Completeness I mentioned that there was a related question I wanted to ask, but would keep separate. I have been recently studying "non-well ordered sets" and Chapter 7 ...
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A truth definition, wrong, but where

Consider the theory ZFC of language with connectives $\neg$, $\rightarrow$, predicative symbol $\in$ and quantifier $\forall$. Assume that we are working in ZFC. Let $\mathcal{V}$ be the class of ...
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Consistency result vs. True in every model of Axiom X

Suppose a forcing extension of ZFC has been found which satisfies statement $A$. For example, say the extension is formed by Cohen or Laver forcing, so that the model satisfies $\neg$CH. At this ...