A necessary condition for a property of cardinal numbers to be a large cardinal property is that the existence of such a cardinal is not known to be inconsistent with ZFC and it has been proven that i ...
The first core model was Kurt G?del's constructible universe L. Ronald Jensen proved the covering lemma for L in the 1970s under the assumption of the non-existence of zero sharp, establishing that L ...
Mathematical topics typically emerge and evolve through interactions among many researchers. Set theory, however, was founded by a single paper in 1874 by Georg Cantor: "On a Characteristic Property o ...
Van der Waerden's theorem states that for any positive integers r and k there exists a positive integer N such that if the integers {1, 2, ..., N} are colored, each with one of r different colors, the ...
The numbers R(r,s) in Ramsey's theorem (and their extensions to more than two colours) are known as Ramsey numbers. An upper bound for R(r,s) can be extracted from the proof of the theorem, and other ...
A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a ...
Euler's conjecture (Waring's problem)Euler's sum of powers conjecture(Also see Euler's conjecture.)Euler's equations Euler's equation – usually refers to Euler's equations (rigid body dynamics), Eule ...
Partial differential equations (PDEs) are equations that involve rates of change with respect to continuous variables. The position of a rigid body is specified by six numbers, but the configuration o ...
In number theory, the Elliott–Halberstam conjecture is a conjecture about the distribution of prime numbers in arithmetic progressions. It has many applications in sieve theory. It is named for Peter ...
It is conjectured that if{2n-1 \choose n-1} \equiv 1 \pmod{n^k},when k=3, then n is prime. The conjecture can be understood by considering k = 1 and 2 as well as 3. When k = 1, Babbage's theorem impli ...
If an denotes the n-th element of the sequence, then an is the least prime factor of\left(\prod_{i n} a_i\right)+1\,.The first element is therefore the least prime factor of the empty product plus on ...
Goldbach's conjecture Vinogradov's theorem proves Goldbach's weak conjecture for sufficiently large n. Deshouillers, Effinger, te Riele and Zinoviev conditionally proved the weak conjecture under the ...
In number theory, Polignac's conjecture was made by Alphonse de Polignac in 1849 and states:For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are in ...
A Fortunate number, named after Reo Fortune, for a given positive integer n is the smallest integer m 1 such that pn# + m is a prime number, where the primorial pn# is the product of the first n prim ...
In mathematics, a Riesel number is an odd natural number k for which the integers of the form k·2n ? 1 are composite for all natural numbers n (sequence A076337 in OEIS).In other words, when k is a ...
