Higher-Order Logic

Eight Faces of Induction: Equivalent Principles...

Andy Cavallo

Let ℕ = {0,1,2,…}. (If you start at 1, shift base cases accordingly.) This post proves that eight standard principles are all equivalent—different faces of the well-foundedness of (ℕ, ≤)....

Eight Faces of Induction: Equivalent Principles...

Andy Cavallo

Let ℕ = {0,1,2,…}. (If you start at 1, shift base cases accordingly.) This post proves that eight standard principles are all equivalent—different faces of the well-foundedness of (ℕ, ≤)....

Strong and Weak Completeness in Classical Highe...

Andy Cavallo

Note: This article is part of an ongoing blog series on higher-order logic, written as a companion to my book Gödel’s God Theorem. This series is not being written in...

Strong and Weak Completeness in Classical Highe...

Andy Cavallo

Note: This article is part of an ongoing blog series on higher-order logic, written as a companion to my book Gödel’s God Theorem. This series is not being written in...