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An idealized computing machine consisting of a fixed set of data registers and set of instructions for operating on them. Register machines are also known as counter machines ...

Church proved several important theorems that now go by the name Church's theorem. One of Church's theorems states that there is no consistent decidable extension of Peano ...

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

Set theory is the mathematical theory of sets. Set theory is closely associated with the branch of mathematics known as logic. There are a number of different versions of set ...

Let A be a relational system, and let L be a language which is appropriate for A. Let phi be a well-formed formula of L, and let s be a valuation in A. Then A|=_sphi is ...

Sudoku (literally, "single number"), sometimes also is a pencil-and-paper logic puzzle whose goal is to complete a grid satisfying various constraints. In the "classic" ...

Let R be the class of expressions generated by 1. The rational numbers and the two real numbers pi and ln2, 2. The variable x, 3. The operations of addition, multiplication, ...

There exists a total computable predicate P such that for any algorithm computing P(x) with running time T(x), there exists another algorithm computing P(x) with computation ...

Capable of taking on one out of two possible values.

If the consistency of one of two propositions implies the consistency of the other, the first is said to have greater consistency strength.