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A recursively enumerable theory without a decidable set of axioms.

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#logic #first-order-logic #computability #decidability
97
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Describe a lattice using predicate language

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#discrete-mathematics #logic #first-order-logic #predicate-logic #order-theory
783
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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
166
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If we have a structure with just relations, then every subset is a substructure?

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#logic #first-order-logic #model-theory
114
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XOR with three constants in First Order Logic

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#notation #first-order-logic
215
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Formal Deduction -

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#logic #first-order-logic #predicate-logic
1.8k
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Proof for Negation of existential quantifier : Formal Deduction && Predicate Logic

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#logic #first-order-logic #predicate-logic #quantifiers #natural-deduction
13
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Notation for indicating a multi-parameter function is bijectivewhen all but one parameter is held constant

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#first-order-logic
203
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Bourbaki theory of set question

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#elementary-set-theory #first-order-logic #predicate-logic
230
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Replacing Predicates in First Order Statements to Produce a Counter-Example World

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#logic #examples-counterexamples #first-order-logic
130
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How sequent calculus are connected with the usual notion of satisfiability or validitiy of formula?

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#logic #propositional-calculus #first-order-logic #proof-theory
614
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Quantifier order for prenex normal form

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#logic #first-order-logic #predicate-logic #quantifiers
42
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$\Sigma \vDash \exists x a(x)$ if and only if $\Sigma \vDash (\neg \forall x( \neg a(x))).$

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#logic #proof-explanation #first-order-logic
180
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Is the set of bounded quantified sentences decidable in PA

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#proof-verification #logic #first-order-logic #peano-axioms
651
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CNF with Nested Quantifiers

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#logic #first-order-logic #predicate-logic #quantifiers #conjunctive-normal-form

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