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Homography in ℝℙ

Roland Coghetto (2016)

Formalized Mathematics

The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7], [16], [17]....

Homology theory in the alternative set theory I. Algebraic preliminaries

Jaroslav Guričan (1991)

Commentationes Mathematicae Universitatis Carolinae

The notion of free group is defined, a relatively wide collection of groups which enable infinite set summation (called commutative π -group), is introduced. Commutative π -groups are studied from the set-theoretical point of view and from the point of view of free groups. Commutativity of the operator which is a special kind of inverse limit and factorization, is proved. Tensor product is defined, commutativity of direct product (also a free group construction and tensor product) with the special...

Horizontal sums of basic algebras

Ivan Chajda (2009)

Discussiones Mathematicae - General Algebra and Applications

The variety of basic algebras is closed under formation of horizontal sums. We characterize when a given basic algebra is a horizontal sum of chains, MV-algebras or Boolean algebras.

How many normal measures can ω + 1 carry?

Arthur W. Apter (2006)

Fundamenta Mathematicae

We show that assuming the consistency of a supercompact cardinal with a measurable cardinal above it, it is possible for ω + 1 to be measurable and to carry exactly τ normal measures, where τ ω + 2 is any regular cardinal. This contrasts with the fact that assuming AD + DC, ω + 1 is measurable and carries exactly three normal measures. Our proof uses the methods of [6], along with a folklore technique and a new method due to James Cummings.

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