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Defining negative integers and rationals in first order logic

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#first-order-logic
104
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A finite axiomatization of $\mathbb N$ and two non-standard models

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#logic #first-order-logic #model-theory #axioms #natural-numbers
30
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Showing that if $M,s \vDash \exists x \varphi$ then $N,s \vDash \exists x \varphi$

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#logic #first-order-logic #predicate-logic #model-theory #quantifiers
125
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Consider the string $(∀x)(∀y)(f(x) = y → ((∀z)g(z) = f(x) ≡ (∀z)g(z) = y))$

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#first-order-logic #predicate-logic #quantifiers
593
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What represents $\exists xP(x)\wedge\neg\exists yQ(y)\wedge\forall z(P(z)\Rightarrow Q(z))$ in $\mathbb R$?

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#logic #first-order-logic #predicate-logic #quantifiers
370
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How to unify a pair of atomic formulas?

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#logic #algorithms #computer-science #first-order-logic #unification
39
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Why is being a free variable a necessary condition

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#logic #first-order-logic
238
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Inductive first-order formula construction

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#logic #first-order-logic
106
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Showing a theory has $\aleph_0$ structures

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#logic #first-order-logic
135
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Logical Validity of predicate logic argument

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#discrete-mathematics #logic #first-order-logic #predicate-logic
59
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Constructing First Order Logic sentence to describe a difference between $\mathbb{Z}$ and $\mathbb{C}$

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#abstract-algebra #logic #first-order-logic
58
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Is it true that for a structure $\mathcal A$ we have $\mbox{Th}(\mathcal A)$ is r.e. iff it is recursive

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#proof-verification #logic #first-order-logic #proof-theory
60
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Natural numbers in discrete maths problem

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#discrete-mathematics #logic #first-order-logic #logic-translation
776
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Why is first order logic not categorical, as Löwenheim-Skolem just reduces the infinity to infinitely countable

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#logic #first-order-logic #model-theory
777
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Uniqueness quantification definition

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

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