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Are there situations outside of set theory where it would be useful if $\mathrm{ICF}$ were true?

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#set-theory
1.4k
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Kunen "Set Theory" 2011 versus 1980 edition - worth buying again?

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#soft-question #set-theory
104
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How do we externalize an element of a model of ZFC?

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#set-theory
101
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Is the size of any set constructible from the set of natural numbers?

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#set-theory
967
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Book/Books leading up to the the axiom of choice?

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#reference-request #set-theory #self-learning #book-recommendation #axiom-of-choice
73
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A problem about filters and ultrafilters

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#set-theory #filters
66
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An other question about filters and ultrafilters

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#set-theory #filters
119
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How to extract the sets "produced" by a axiomatic set theory, into some newly introduced collection?

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#logic #set-theory #predicate-logic #axioms #type-theory
329
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How are models constructed?

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#logic #set-theory #model-theory
1k
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Different definitions of P-Points (ultrafilters)

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#general-topology #set-theory #filters
67
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Can we define ordinals such that the following sentences are independent of ZFC?

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#set-theory #cardinals
470
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Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$

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#set-theory #intuition #cardinals #axiom-of-choice
327
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P-generic filter

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#set-theory #forcing
2k
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$\mathsf{ZF}$ is not finitely axiomatizable

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#logic #set-theory
70
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The Categories $\mathrm{Set}\times\mathrm{Set}$ and $\mathrm{Set}+\mathrm{Set}$

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#category-theory #set-theory

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