# Tagged Questions

This tag is for set theory topics typically studied at the advanced undergraduate or graduate level. These include cofinality, axioms of ZFC, axiom of choice, forcing, set-theoretic independence, large cardinals, models of set theory, ultrafilters, ultrapowers, constructible universe, inner model ...

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### Why do we need to learn Set Theory?

I was planning to write some article for the Mathematics magazine of our college and it occurred to me that it will be a good idea to write about the impact and importance of Set Theory. I plan ...
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### Cardinality of the base of a ring of sets

Concretely, my question is: What is the size of the minimal base of a ring of sets? In my understanding the base is the set of elements that can be used to "deduce the rest". E.g., if I have a ring ...
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### Axiom of Regularity

I am having difficulty understanding Axiom of Regularity : Every non-empty set $\rm A$ contains an element $\rm B$ which is disjoint from $\rm A.$ So from my understanding if I have a set like: ...
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### What are the consequences if Axiom of Infinity is negated?

What mathematics can be built with standard ZFC with Axiom of Infinity replaced with its negation? Can the analysis be built? Is there special name for "ZFC without Infinity" set theory? I also ...
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### Prikry Hypothesis implies Kurepa Hypothesis

I want to show that $\textbf{HP}_\kappa$ implies $\textbf{HK}_\kappa$, Prikry hypothesis and Kurepa hypothesis in $\kappa$, respectively. Where \textbf{HK}_\kappa: \text{ There's a ...
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### Jech 3rd Edition Section 12 page 162 Models of Set Theory

Jech page 162 states : Let Form denote the set of all formulas of the language {$\in$}. As with any actual (metamathematical) natural number we can associate the corresponding element of N (i.e. the ...