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How badly does foundation fail in NF(etc.)?

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#logic #set-theory #axioms #foundations #alternative-set-theories
168
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Alternative axioms for NBG or MK

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#set-theory #axioms #foundations
135
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On independency of ZFC of statements in math problem solving

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#logic #axioms #provability
118
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Definition of rational numbers

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#definition #rational-numbers #axioms #ordered-fields
156
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Basic division and multiplication

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#arithmetic #axioms
97
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Show that first order Peano's axioms capture the natural numbers regarding satisfiablity

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#logic #arithmetic #first-order-logic #axioms #peano-axioms
204
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Taking an unproven but "seemingly true" statement as an axiom

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#first-order-logic #predicate-logic #axioms #goldbachs-conjecture
1.2k
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Reduced homology of a point is trivial from axioms

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#algebraic-topology #homology-cohomology #homological-algebra #axioms
215
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intuition for PFA

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#set-theory #axioms #forcing #large-cardinals
550
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Excess axioms in the definition of a metric

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#metric-spaces #definition #axioms
95
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When Can You State that a Given Class is a Set?

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#set-theory #axioms
132
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finding structures where the singleton axiom, the axiom of extensionality and the axiom of empty set do hold

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#set-theory #axioms
789
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Example of a set of real numbers that is Dedekind-finite but not finite

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#set-theory #infinity #axiom-of-choice #axioms
143
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Reining in the Axiom of Power Set in ZF

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#set-theory #axioms
154
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Why is "If ψ ∈ Γ then the sequent (Γ ⊢ ψ) is correct" true?

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#logic #definition #axioms #natural-deduction #sequent-calculus

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