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Why is $\sf MM^{++}$ the strongest forcing axiom?

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#set-theory #axioms #forcing
140
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Names for two Basic axioms for Propositional Logic

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#logic #terminology #propositional-calculus #axioms
567
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Is "substitution" an axiom?

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#proof-explanation #relations #axioms
76
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Decidability of redundancy of axiom in classical propositional logic

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#logic #computer-science #axioms #turing-machines
89
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$AC_\omega$ is weaker than $AC$, though not provable in ZF without $AC$?

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#logic #set-theory #axiom-of-choice #axioms
199
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clarification on axiom of regularity

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#set-theory #axioms
131
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Is there any reason why the continuum hypothesis cannot be taken as a postulate which may or may not be true?

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#set-theory #axioms
289
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How many axioms are in ZFC, and is ZFC a decidable language?

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#set-theory #axioms
143
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Is this the Axiom of Infinity?

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#elementary-set-theory #set-theory #terminology #axioms
114
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Axiom of foundation implies that bottomless sets are empty?

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#elementary-set-theory #set-theory #terminology #self-learning #axioms
60
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Is the class of ordinals part of the class of sets in NBG set theory?

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#elementary-set-theory #axioms #foundations
186
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How do we know inference rules are correct?

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#logic #proof-writing #axioms #natural-deduction
84
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Equational axioms for quantifiers

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#logic #predicate-logic #quantifiers #axioms #algebraic-logic
152
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Can we axiomatize the complex numbers without directly defining the reals?

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#analysis #axioms #foundations #second-order-logic
72
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Stronger versions of the Power Set Axiom?

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#model-theory #axioms

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