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Does the theory of infinite sets in the language of pure equality have a non-redundant axiomatization?

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#first-order-logic
225
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Nonexistence of independent axiomatization of a theory in a finite language.

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#first-order-logic
55
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Logic statements equivalence

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#general-topology #first-order-logic #second-order-logic
88
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How to express "A is B" in first order logic

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#first-order-logic
67
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Prenex form of uniqueness quantifier

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#first-order-logic
135
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Completeness of first-order logic with interpreted function symbols

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#logic #first-order-logic
198
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First-order logic and Peano Arithmetic paradox

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#logic #induction #first-order-logic #peano-axioms
47
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What does $\exists !x(P\rightarrow Q(x))$ translate to? A paradox?

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#first-order-logic
84
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How to show conservative extension without resorting to model theory?

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#logic #first-order-logic #proof-theory
95
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Completeness theorem: validity in some non-empty domain

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#logic #first-order-logic #predicate-logic #meta-math
879
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How to determine the validity of statements in First Order Logic. Is there a general method?

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#discrete-mathematics #logic #first-order-logic #predicate-logic
13
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What is the formal translation of this statement?

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#first-order-logic
375
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Mathematical Logic (Shoenfield) : Lemma 1

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#logic #first-order-logic #predicate-logic
566
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Is there any way to reduce standard second-order logic to first-order logic?

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#logic #first-order-logic #second-order-logic
76
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Quantifier difference notation

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#logic #first-order-logic #predicate-logic #quantifiers

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