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15
103
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Axiom Schema of Separation in ZF and phrasing Russel's Property

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#set-theory #axioms
68
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$v_2$ is not substitutable for $v_1$ in $\forall \,v_1\,\forall\,v_2\,Bv_1v_2\to\forall v_2 Bv_2v_2$

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#logic #axioms #substitution
64
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Proof of uniqueness of positive cubes

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#real-analysis #general-topology #axioms
348
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What elementary theorems depend on the Axiom of Infinity?

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#axioms #foundations
92
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How simple it can be?

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#axioms #incompleteness
97
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Alternate definition of fields

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#abstract-algebra #group-theory #field-theory #axioms
315
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Are there any alternative axioms for Euclidean geometry?

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#euclidean-geometry #axioms
119
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Is it true that $0\in 1$?

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#elementary-set-theory #axioms #peano-axioms
45
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Does axiom P hold for the set of Rational Polynomials?

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#abstract-algebra #polynomials #axioms
112
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Is there a finite axiomatization of Tarski's geometry axioms?

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#geometry #euclidean-geometry #first-order-logic #axioms #axiomatic-geometry
49
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How quickly can EFA define things, asymptotically?

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#asymptotics #arithmetic #axioms #elementary-functions #meta-math
588
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Exercises and solutions for natural deduction proofs in Robinson and Peano arithmetic

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#logic #reference-request #axioms #peano-axioms #natural-deduction
912
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Can we axiomatize a field starting with the binary operations and only “equational” axioms?

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#abstract-algebra #reference-request #field-theory #axioms #universal-algebra
192
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Language of an Axiomatic System in the Incompleteness Theorem

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#logic #examples-counterexamples #axioms #incompleteness #formal-systems
3k
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Prove addition is commutative using axioms, definitions, and induction

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#real-analysis #proof-verification #axioms #peano-axioms #natural-numbers

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