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Is $\Bbb R$ definable in $(\Bbb C,0,1,+,*,\exp)$?

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#logic #model-theory #first-order-logic
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Equivalent expressions for $\lnot (\forall x)\exists y A $

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#logic #quantifiers #predicate-logic #first-order-logic
55
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A form of compactness?

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#logic #first-order-logic
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first-order logic: Any finite set of first-order sentences true in all divisible abelian groups is true in some non-divisable one.

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#group-theory #logic #model-theory #first-order-logic
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A first order theory whose finite models are exactly the $\Bbb F_p$

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#logic #field-theory #finite-fields #model-theory #first-order-logic
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A *finite* first order theory whose finite models are exactly the $\Bbb F_p$?

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#logic #field-theory #finite-fields #model-theory #first-order-logic
878
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Proving Tychonoff's theorem with the Compactness theorem of logic

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#general-topology #logic #compactness #model-theory #first-order-logic
198
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First order logic, finite partially ordered structure problem

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#logic #model-theory #first-order-logic
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Is "$\subset$" a symbol of first-order language of set theory?

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#elementary-set-theory #logic #first-order-logic
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What is the difference in the meaning of equality symbol "$=$" as a logical symbol vs. a parameter?

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#logic #first-order-logic
208
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Meaning of the formula $\exists x\exists x P(x)$

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#logic #first-order-logic
617
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Is this formula logically valid

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#logic #predicate-logic #first-order-logic
8.4k
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Best method to determine if a first order formula is logically valid?

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#logic #predicate-logic #first-order-logic
60
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Justify conditional

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#logic #predicate-logic #first-order-logic
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Is there a 0-1 law for the theory of groups?

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#group-theory #logic #finite-groups #model-theory #first-order-logic

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