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does deductive completeness implies semantic completeness

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#logic #first-order-logic #model-theory #meta-math
130
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The construction of the term model in completeness proofs of FOL

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#first-order-logic #model-theory
102
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$f$ has a left inverse iff $f$ is injective

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#real-analysis #functions #logic #first-order-logic
77
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Equivalence between a first-order formula and an infinitary formula modulo a theory

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#logic #first-order-logic #model-theory
97
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Prove that every tautology of the form (α → β) can be broken into (α → γ) and (γ → β), where the variables in γ aren’t in exactly one of α and β

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#logic #propositional-calculus #first-order-logic
77
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The union of the power set of a family of sets

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#logic #first-order-logic
179
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Treatment of mathematical logic with less bookkeeping?

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#logic #soft-question #first-order-logic #model-theory
23
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Quantify in logic over elements of cartesian product such that they fulfill specifc properties

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#logic #first-order-logic #order-theory #quantifiers #second-order-logic
48
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Equivalent condition for a sentence to be universally valid

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#logic #first-order-logic #model-theory
102
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What is the standard notation for “for some number”?

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#notation #first-order-logic
104
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Changing the ∀ quantifier to the ∃ quantifier

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#logic #first-order-logic #quantifiers
123
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Absurd argument showing every first-order theory is consistent

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#logic #first-order-logic #model-theory
98
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How to prove Gödel's Completeness Theorem apply for uncountable language?

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#logic #first-order-logic
92
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Prove that if $\mathcal L$ is the empty language and $C$ is the set of structures $\mathcal M_n := \{1,...,n\}$ then $\text{Th}_a(C)$ is complete

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#logic #first-order-logic #model-theory
54
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Exact meaning of terms in First-Order Logic

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#logic #first-order-logic #formal-grammar

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