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On the number of Russell’s socks or $2 + 2 + 2 + \dots = ?$

Horst Herrlich, Eleftherios Tachtsis (2006)

Commentationes Mathematicae Universitatis Carolinae

The following question is analyzed under the assumption that the Axiom of Choice fails badly: Given a countable number of pairs of socks, then how many socks are there? Surprisingly this number is not uniquely determined by the above information, thus giving rise to the concept of Russell-cardinals. It will be shown that: • some Russell-cardinals are even, but others fail to be so; • no Russell-cardinal is odd; • no Russell-cardinal is comparable with any cardinal of the form $ℵ_{α}$ or $2^{ℵ_{α}}$ ; • finite sums...

On the open-open game

Peg Daniels, Kenneth Kunen, Haoxuan Zhou (1994)

Fundamenta Mathematicae

We modify a game due to Berner and Juhász to get what we call “the open-open game (of length ω)”: a round consists of player I choosing a nonempty open subset of a space X and II choosing a nonempty open subset of I’s choice; I wins if the union of II’s open sets is dense in X, otherwise II wins. This game is of interest for ccc spaces. It can be translated into a game on partial orders (trees and Boolean algebras, for example). We present basic results and various conditions under which I or II...

On the Order Type L-valued Relations on L-powersets.

I. Uljane (2007)

Mathware and Soft Computing

On the orthogonalization of arbitrary Boolean formulae.

Bruni, Renato (2005)

Journal of Applied Mathematics and Decision Sciences

On the Paradox of Confirmation.

J. Canfield (1962)

Metrika

On the planarity of the equilateral, isogonal pentagon.

Pambuccian, Victor (2003)

Mathematica Pannonica

On the ◊ principle

Adam Piołunowicz (1984)

Fundamenta Mathematicae

On the principle square : coding and extending embeddings

L. J. Stanley (1976)

Annales scientifiques de l'Université de Clermont. Mathématiques

On the problem of axiomatization of tame representation type

Stanisław Kasjan (2002)

Fundamenta Mathematicae

Associative algebras of fixed dimension over algebraically closed fields of fixed characteristic are considered. It is proved that the class of algebras of tame representation type is axiomatizable. Moreover, finite axiomatizability of this class is equivalent to the conjecture that the algebras of tame representation type form a Zariski-open subset in the variety of algebras.