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A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let phi_x^((k)) denote the recursive function of k variables with ...

The Kreisel conjecture is a conjecture in proof theory that postulates that, if phi(x) is a formula in the language of arithmetic for which there exists a nonnegative integer ...

Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...

Three guests decide to stay the night at a lodge whose rate they are initially told is $30 per night. However, after the guests have each paid $10 and gone to their room, the ...

A plot of the cells on a grid satisfying bitwise XOR(a,b)<n for consecutive values of n=1, 2, .... It is thought that it was discovered by Jackson Wright on the RLE PDP-1 ...

A paradox in decision theory. Given two boxes, B1 which contains $1000 and B2 which contains either nothing or a million dollars, you may pick either B2 or both. However, at ...

The theory of natural numbers defined by the five Peano's axioms. Paris and Harrington (1977) gave the first "natural" example of a statement which is true for the integers ...

A set S of integers is said to be recursive if there is a total recursive function f(x) such that f(x)=1 for x in S and f(x)=0 for x not in S. Any recursive set is also ...

If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a ...

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, ...