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"Every set is equinumerous to a well-founded set" - provable in $\sf ZF-Reg$?

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#logic #set-theory #axioms
284
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Why is the axiom of pairing needed in Von Neumann-Godel-Bernays Set Theory?

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#set-theory #axioms
492
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How do we know that our definitions/axioms are not contradictory?

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#group-theory #logic #definition #first-order-logic #axioms
5.9k
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Difference between Logical Axioms and Rules of Inference

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#logic #propositional-calculus #axioms #natural-deduction #hilbert-calculus
82
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Are there unsolved problems known to be not independent of the axiomatic system it is proposed in?

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#big-list #axioms
287
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The order isomorphism theorem without Replacement

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#set-theory #order-theory #ordinals #axioms
395
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$A=\{A,\emptyset\}$ and axiom of regularity

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#elementary-set-theory #axioms
1.6k
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What is the definition of axiom (mathematically speaking)

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#definition #axioms
345
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Does the Russell Set exist?

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#elementary-set-theory #axioms #paradoxes
5.3k
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Foundation of ordering of real numbers

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#real-analysis #order-theory #real-numbers #axioms #foundations
192
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Algebraic structures and axiomatic systems

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#abstract-algebra #axioms #binary-operations
1.3k
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How can the axiom of choice be called "axiom" if it is false in Cohen's model?

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#logic #terminology #axioms
274
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Alternate Axiom of Infinity

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#elementary-set-theory #infinity #axioms
149
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A familiar quasigroup - about independent axioms

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#abstract-algebra #axioms #quasigroups
463
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Can the generalized continuum hypothesis be disguised as a principle of logic?

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#soft-question #set-theory #axiom-of-choice #axioms #philosophy

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