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15
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Can we have a Choice-AntiChoice chain?

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#set-theory #first-order-logic #axiom-of-choice
234
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Constructive proof of the Banach-Alaouglu theorem

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#functional-analysis #banach-spaces #axiom-of-choice #separable-spaces #reverse-math
203
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Is Axiom of Choice necessary with this particular quotient set?

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#logic #set-theory #equivalence-relations #axiom-of-choice
187
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Explicit example of an additive map which is not R-linear

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#linear-algebra #axiom-of-choice
71
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Proving one specific equivalent formulation of AC

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#set-theory #axiom-of-choice
89
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Can the following sequence be shown to necessarily exist w/o AoC?

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#sequences-and-series #analysis #set-theory #axiom-of-choice
289
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Developing intuition for a world without AC

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#reference-request #set-theory #self-learning #axiom-of-choice
3.5k
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Why does Zorn's Lemma fail to produce a largest group?

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#group-theory #elementary-set-theory #axiom-of-choice
166
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How to prove Baire Category theorem by Zorn's lemma?

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#general-topology #axiom-of-choice #baire-category
152
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Can there be an infinite $\kappa$ with $\kappa\to(\omega)^\omega_2$ in $\mathsf{ZF}$?

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#set-theory #axiom-of-choice
129
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Is $\aleph_1\cdot\mathfrak c=2^\mathfrak c$ consistent with ZF?

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#set-theory #axiom-of-choice
338
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The Scope of Axiomatic Set Theory

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#logic #set-theory #axiom-of-choice #foundations
88
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Procedure for producing a total order on infinite set

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#logic #axiom-of-choice
275
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Have I proved in ZF $\aleph (X) \lt \aleph (\mathscr P^3(X))$?

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#proof-verification #set-theory #axiom-of-choice
210
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Extension of a linear map in a generic vector space (without Zorn's lemma)

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#linear-algebra #functional-analysis #linear-transformations #axiom-of-choice #hahn-banach-theorem

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