Mycielski ideal and the perfect set theorem
نویسندگان
چکیده
منابع مشابه
The Perfect Set Theorem and Definable Wellorderings of the Continuum
Let r be a collection of relations on the reals and let M be a set of reals. We call M a perfect set basis for r if every set in r with parameters from M which is not totally included in M contains a perfect subset with code in M. A simple elementary proof is given of the following result (assuming mild regularity conditions on r and M): If M is a perfect set basis for r, the field of every wel...
متن کاملAn extension of Lehman's theorem and ideal set functions
Lehman's theorem on the structure of minimally nonideal clutters is a fundamental result in polyhedral combinatorics. One approach to extending it has been to give a common generalization with the characterization of minimally imperfect clutters [15, 8]. We give a new generalization of this kind, which combines two types of covering inequalities and works well with the natural de nition of mino...
متن کاملThe Perfect Number Theorem and Wilson's Theorem
This article formalizes proofs of some elementary theorems of number theory (see [1, 26]): Wilson’s theorem (that n is prime iff n > 1 and (n − 1)! ∼= −1 (mod n)), that all primes (1 mod 4) equal the sum of two squares, and two basic theorems of Euclid and Euler about perfect numbers. The article also formally defines Euler’s sum of divisors function φ, proves that φ is multiplicative and that ...
متن کاملOn the Leibniz - Mycielski Axiom in Set Theory ∗
Motivated by Leibniz’s thesis on the identity of indiscernibles, Mycielski introduced a set theoretic axiom, here dubbed the Leibniz-Mycielski axiom LM, which asserts that for each pair of distinct sets x and y there exists an ordinal α exceeding the ranks of x and y, and a formula φ(v), such that (V α ,∈) satisfies φ(x) ∧ ¬φ(y) . We examine the relationship between LM and some other axioms of ...
متن کاملGENERALIZED PRINCIPAL IDEAL THEOREM FOR MODULES
The Generalized Principal Ideal Theorem is one of the cornerstones of dimension theory for Noetherian rings. For an R-module M, we identify certain submodules of M that play a role analogous to that of prime ideals in the ring R. Using this definition, we extend the Generalized Principal Ideal Theorem to modules.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2004
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-04-07360-5