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Decision procedure in Presburger arithmetic

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#logic #proof-theory #presburger-arithmetic
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Showing that Presburger arithmetic is decidable by deciding if $\mathbb N \models \varphi$, but does it give provability in the axioms?

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#logic #first-order-logic #proof-theory #decidability #presburger-arithmetic
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Strongest decidable system of arithmetics

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#logic #peano-axioms #presburger-arithmetic
118
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Systems of arithmetic models

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#logic #first-order-logic #model-theory #peano-axioms #presburger-arithmetic
247
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Do induction axioms of Peano Arithmetic have other simple equivalent forms?

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#logic #induction #peano-axioms #presburger-arithmetic
141
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Why Presburger arithmetic cannot prove pigeonhole principle

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#logic #peano-axioms #provability #presburger-arithmetic
170
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How much arithmetic is required to formalize quantifier elimination in Presburger arithmetic?

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#logic #proof-theory #reverse-math #quantifier-elimination #presburger-arithmetic
433
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Are there "interesting" theorems in Peano arithmetic, that only use the addition operation?

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#elementary-number-theory #soft-question #induction #peano-axioms #presburger-arithmetic
136
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Graph planarity definability clarification in literature?

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#graph-theory #first-order-logic #planar-graphs #second-order-logic #presburger-arithmetic
69
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Finding simpler implied formulas while preserving contradiction

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#logic #presburger-arithmetic
106
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Different arithmetics

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#reference-request #arithmetic #peano-axioms #presburger-arithmetic
221
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An impressive fact expressible in Presburger arithmetic?

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#logic #arithmetic #model-theory #automated-theorem-proving #presburger-arithmetic
156
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Oracle for computing transitive closure of presburger arithmetic formula if it exists: Computable?

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#logic #computability #presburger-arithmetic
190
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Question concerning Presburger arithmetic

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#logic #first-order-logic #model-theory #presburger-arithmetic
103
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Doubly exponential complexity of Presburger arithmetics

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#logic #computational-complexity #first-order-logic #presburger-arithmetic

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