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Predicate logic, path length with $2$ variables

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#logic #first-order-logic #predicate-logic
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How is induction used in this proof?

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#induction #first-order-logic
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Is proof of the law of identity a case of circular reasoning?

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#logic #solution-verification #proof-explanation #first-order-logic #philosophy
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How to show that Second Order Logic is more expressive than Weak Second Order Logic

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#first-order-logic #higher-order-logic
69
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If $f(x)=x$, then it is injective, which is stated as $(f(x_1)=f(x_2)\implies (x_1=x_2)$. Does this allow antecedent false and consequent true?

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#logic #propositional-calculus #first-order-logic
118
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Representability of Goodstein function in PA

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#logic #first-order-logic #computability #peano-axioms
175
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If Goldbach's conjecture G is undecidable in PA, then can we prove $\mathbb N\models G$?

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#first-order-logic #model-theory #peano-axioms #incompleteness #nonstandard-models
41
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Strong homogeneity of order type of real closed fields

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#first-order-logic #model-theory #ordered-fields
51
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Construct a sentence involving a model's function's injective character implicating the model's universe's infinity

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#logic #first-order-logic #model-theory
52
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Fitch-style set theory proofs

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#first-order-logic
168
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Why are logical equality axioms about variables and not terms?

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#first-order-logic #axioms
189
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What is a "class model" exactly?

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#set-theory #first-order-logic #model-theory #meta-math
43
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checking the correctness of a sequential calculus

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#logic #first-order-logic
38
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Formal deduction of some basic identities that rearrange the universal quantifier

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#first-order-logic #predicate-logic #natural-deduction
185
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What exactly is meant by 'sentence' and 'expression'?

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#logic #terminology #propositional-calculus #first-order-logic

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