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Another way for partition of perfect set

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#real-analysis #set-theory #axioms #descriptive-set-theory #transfinite-induction
37
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Why finding an undecidable proposition doesn't imply consistency, if anything is provable in an inconsistent axiomatic system?

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#logic #set-theory #axioms
104
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About ZFC and Partition perfect set into perfect sets

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#general-topology #set-theory #axioms #descriptive-set-theory
44
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Non-contradictory axiom system for a binary operation

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#model-theory #integers #axioms #binary-operations
242
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Is it really important to do axiomatic study of real numbers before learning Calculus?

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#calculus #algebra-precalculus #real-numbers #axioms
91
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Proof of Well-Ordering, without Induction, by the Least Upper Bound Axiom

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#real-analysis #analysis #induction #axioms
82
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Modus ponens rule

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#logic #propositional-calculus #axioms
72
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Do tree choice lead to set choice?

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#graph-theory #set-theory #axiom-of-choice #axioms
1.3k
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The empty set fails to satisfy only one of the axioms of vector spaces. Which one? ("Linear Algebra Done Right" by Sheldon Axler.)

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#vector-spaces #axioms
92
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Is the axiom of regularity/foundation equivalent to $\forall x:x\notin x$?

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#elementary-set-theory #set-theory #axioms #foundations
29
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Infinity axioms with one function symbol

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#logic #first-order-logic #infinity #axioms
206
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Simplest set of axioms and inference rules for first-order logic?

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#first-order-logic #axioms #foundations #formal-proofs #formal-systems
55
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Existence of a countably infinite set in weakened versions of $\mathsf{ZFC}$

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#set-theory #axioms
37
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Can the existence of $\omega$ be derived from this alternate axiom of infinity?

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#set-theory #infinity #ordinals #axioms
181
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Is there a succinct way to axiomatize the theory of a single elementary topos?

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#logic #category-theory #axioms #topos-theory

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