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Non-standard model of arithmetic - why is adding new constants to the model acceptable?

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#logic #first-order-logic #model-theory #nonstandard-models
57
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SAT preserving conversion of statement to existential one

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#logic #first-order-logic #decidability
112
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Translating Propositional Functions

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#logic #propositional-calculus #predicate-logic #first-order-logic #quantifiers
92
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Write two models of the language

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#logic #first-order-logic #model-theory #formal-languages
69
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Write mathematical formula for: not every square root of a positive number is positive number

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#logic #first-order-logic
589
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Defining first order logic quantifiers without sets

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#logic #set-theory #predicate-logic #first-order-logic #foundations
124
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Theory $T$ has model isomorphic with its proper substructure. Prove that $T$ has infinite model isomorhpic with its proper substructure.

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#logic #first-order-logic #model-theory
330
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Homomorphism between structures in first order logic

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#logic #first-order-logic #model-theory
72
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Is it possible to define an automorphism on the structure $\mathfrak{Q}=(\mathbb{Q},<)$ and what would be an example?

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#abstract-algebra #logic #first-order-logic
171
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Finite structures of a theory have finite atomic diagram.

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#logic #first-order-logic #model-theory
157
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Isomorphism between finite structures which is not elementary

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#first-order-logic #model-theory
96
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Is $\forall_x\forall_y\forall_z\Big(P(x,x)\wedge(P(x,z)\implies\big(P(x,y)\vee P(y,z)\big)\Big)\implies\exists_x\forall_y P(x,y)$ tautology?

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#logic #predicate-logic #first-order-logic #satisfiability
145
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What is $x = x$?

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#predicate-logic #first-order-logic
939
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Contrapositive of a quantified statement

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#logic #first-order-logic #quantifiers
1.1k
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countability of set of well-formed formulas

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#elementary-set-theory #logic #predicate-logic #first-order-logic

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