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What is meant by one axiom being "weaker" than another?

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#logic #set-theory #axioms
118
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Weak classical Deontic Logics

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#logic #axioms #modal-logic
160
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Are forcing techniques possible to automate for mechanized reasoning?

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#logic #axioms #incompleteness #forcing
200
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Help with a proof by induction.

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#induction #self-learning #axioms #peano-axioms
196
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Justification for the Axiom of Union

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#set-theory #axioms
546
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What if we change axiom of arithmetic?

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#arithmetic #axioms
1.6k
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Can multiplication be defined without addition?

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#arithmetic #definition #axioms
199
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Deriving the Axiom of Infinity

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#set-theory #relations #axioms
2.8k
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Can we prove the existence of $A\cup B$ without the union axiom?

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#set-theory #axioms
226
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Does the language of group theory need a constant?

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#group-theory #model-theory #axioms
1.3k
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Describe a sound and complete proof system

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#logic #axioms
5.1k
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Prove if $ac>bc$ and $c>0$, then $a>b$

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#inequality #axioms
698
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Is it possible to formalize the idea that large cardinal axioms don't limit us, while their negations do?

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#set-theory #axioms #foundations #large-cardinals
1.3k
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Prove $x-y=0 \iff x=y$ using only field axioms

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#abstract-algebra #field-theory #axioms
2.5k
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Is axiom of completeness an axiom?

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#real-analysis #axioms

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