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Axiomatisation of first-order free logic

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#first-order-logic
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How to prove that the following simplification rule is satisfiability-equivalent?

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#logic #first-order-logic #computational-complexity #boolean-algebra #satisfiability
156
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Any first-order theory can be interpreted in an extension of $\mathsf{ZFC}$?

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#logic #set-theory #first-order-logic
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What are some surprising theories that contain Robinson arithmetic?

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#first-order-logic #model-theory
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What is the correct way to interpret the Intuitionistic rules of Kleene's sequent (Gentzen) system G1 (in sec. 77 of Kleene I.M. 1952)

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#logic #first-order-logic #proof-theory #intuitionistic-logic #sequent-calculus
78
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Why is $S \models \bot$ the "same" as $S$ has no model?

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#logic #first-order-logic #model-theory
43
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Unique readability of first order languages in Enderton

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#logic #first-order-logic
35
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First order logic formalization problem

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#logic #first-order-logic #automated-theorem-proving #theorem-provers
47
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Meaning of Provable recursiveness

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#number-theory #first-order-logic #computability #peano-axioms #formal-systems
78
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$\forall x(P(x) \rightarrow Q(x))\stackrel{?}{\equiv}\neg\exists x(P(x) \rightarrow \neg Q(x))\stackrel{?}{\equiv}\neg\exists x(P(x) \wedge\neg Q(x))$

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#logic #first-order-logic #quantifiers
60
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Non recursive provably total functions

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#number-theory #first-order-logic #recursion #computability #peano-axioms
46
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Are all Relations statements? Or are all Statements relations?

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#discrete-mathematics #first-order-logic #relations
70
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Axioms for equality

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#first-order-logic #relations #axioms
101
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Translating "nobody likes a sore loser"

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#logic #first-order-logic
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Is it decidable whether a classically valid first-order formula is also intuitionistically valid?

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#logic #first-order-logic #intuitionistic-logic #decidability

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