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Let g(x_1,...,x_n,y) be a function such that for any x_1, ..., x_n, there is at least one y such that g(x_1,...,x_n,y)=0. Then the mu-operator muy(g(x_1,...,x_n,y)=0) gives ...

A sentential formula that contains at least one free variable (Carnap 1958, p. 24). A sentential variable containing no free variables (i.e., all variables are bound) is ...

Proof theory, also called metamathematics, is the study of mathematics and mathematical reasoning (Hofstadter 1989) in a general and abstract sense itself. Instead of ...

Resolution is a widely used word with many different meanings. It can refer to resolution of equations, resolution of singularities (in algebraic geometry), resolution of ...

Building on work of Huntington (1933ab), Robbins conjectured that the equations for a Robbins algebra, commutativity, associativity, and the Robbins axiom !(!(x v y) v !(x v ...

A truth table is a two-dimensional array with n+1 columns. The first n columns correspond to the possible values of n inputs, and the last column to the operation being ...

Consider expressions built up from variables and constants using function symbols. If v_1, ..., v_n are variables and t_1, ..., t_n are expressions, then a set of mappings ...

In predicate calculus, a universal formula is a prenex normal form formula (i.e., a formula written as a string of quantifiers and bound variables followed by a ...

The term used in propositional calculus for the NAND connective. The notation A|B is used for this connective, a most unfortunate choice in light of modern usage of A|B or ...

A man of Seville is shaved by the Barber of Seville iff the man does not shave himself. Does the barber shave himself? This pseudoparadox was proposed by Bertrand Russell.