Deduction theorems within RM and its extensions

1999 ◽  
Vol 64 (1) ◽  
pp. 279-290 ◽  
Author(s):  
J. Czelakowski ◽  
W. Dziobiak
Keyword(s):  
Extension Property ◽  
Infinite Family ◽  
Relevant Logic ◽  
Congruence Extension Property ◽  
Deduction Theorem ◽  
Consequence Operation ◽  
The Family ◽  
Relative Congruence

AbstractIn [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic RM or with the extensions of RM and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if C is a consequence operation with CRM ≤ C and C admits a deduction theorem scheme, then C is equal to a consequence operation specified in [13]. In algebraic terms, this means that the only quasivarieties of Sugihara algebras with the relative congruence extension property are the quasivarieties corresponding, via the algebraization process, to the consequence operations specified in [13].

scholarly journals On the Congruence Extension Property for Semigroups: Preservation under Homomorphic Images

2001 ◽  
Vol 238 (2) ◽  
pp. 411-425
Author(s):  
Xilin Tang
Keyword(s):  
Extension Property ◽  
Congruence Extension Property

From the Outside In

2015 ◽  
Author(s):  
Derek Smith
Keyword(s):  
Positive Integer ◽  
Infinite Family ◽  
Open Problems ◽  
The Family

This chapter discusses Slothouber–Graatsma–Conway puzzle, which asks one to assemble six 1 × 2 × 2 pieces and three 1 × 1 × 1 pieces into the shape of a 3 × 3 × 3 cube. The puzzle has been generalized to larger cubes, and there is an infinite family of such puzzles. The chapter's primary argument is that, for any odd positive integer n = 2k + 1, there is exactly one way, up to symmetry, to make an n × n × n cube out of n tiny 1 × 1 × 1 cubes and six of each of a set of rectangular blocks. The chapter describes a way to solve each puzzle in the family and explains why there are no other solutions. It then presents several related open problems.

Congruences on semigroups with the congruence extension property

1999 ◽  
Vol 27 (11) ◽  
pp. 5439-5461 ◽  
Author(s):  
Xilin Tang
Keyword(s):  
Extension Property ◽  
Congruence Extension Property

Congruence extension property for semirings

2020 ◽  
Vol 15 (8) ◽  
pp. 393-400
Author(s):  
Yun Zhao ◽  
YuanLan Zhou ◽  
Tian Zeng
Keyword(s):  
Extension Property ◽  
Congruence Extension Property

scholarly journals AUTOMORPHISMS OF THE UHF ALGEBRA THAT DO NOT EXTEND TO THE CUNTZ ALGEBRA

2010 ◽  
Vol 89 (3) ◽  
pp. 309-315 ◽  
Author(s):  
ROBERTO CONTI
Keyword(s):  
Sufficient Conditions ◽  
Extension Property ◽  
Cuntz Algebra ◽  
Maximal Abelian Subalgebra ◽  
Abelian Subalgebra ◽  
Matrix Algebras ◽  
The Family ◽  
The Matrix ◽  
Inner Automorphisms ◽  
Necessary And Sufficient

AbstractThe automorphisms of the canonical core UHF subalgebra ℱn of the Cuntz algebra 𝒪n do not necessarily extend to automorphisms of 𝒪n. Simple examples are discussed within the family of infinite tensor products of (inner) automorphisms of the matrix algebras Mn. In that case, necessary and sufficient conditions for the extension property are presented. Also addressed is the problem of extending to 𝒪n the automorphisms of the diagonal 𝒟n, which is a regular maximal abelian subalgebra with Cantor spectrum. In particular, it is shown that there exist product-type automorphisms of 𝒟n that do not extend to (possibly proper) endomorphisms of 𝒪n.

scholarly journals A family of formulas with reversal of high avoidability index

2017 ◽  
Vol 27 (05) ◽  
pp. 477-493 ◽  
Author(s):  
James Currie ◽  
Lucas Mol ◽  
Narad Rampersad
Keyword(s):  
Simple Structure ◽  
Complex Structure ◽  
Infinite Family ◽  
Index Formula ◽  
The Family

We present an infinite family of formulas with reversal whose avoidability index is bounded between [Formula: see text] and [Formula: see text], and we show that several members of the family have avoidability index [Formula: see text]. This family is particularly interesting due to its size and the simple structure of its members. For each [Formula: see text] there are several previously known avoidable formulas (without reversal) of avoidability index [Formula: see text] but they are small in number and they all have rather complex structure.

scholarly journals Perfect 2-Colorings of the Grassmann Graph of Planes

10.37236/8672 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Stefaan De Winter ◽  
Klaus Metsch
Keyword(s):  
Infinite Family ◽  
Grassmann Graph ◽  
The Family

We construct an infinite family of intriguing sets, or equivalently perfect 2-colorings, that are not tight in the Grassmann graph of planes of PG$(n,q)$, $n\ge 5$ odd, and show that the members of the family are the smallest possible examples if $n\ge 9$ or $q\ge 25$.

Linear programming analysis of VA/Q distributions: average distribution

1987 ◽  
Vol 62 (4) ◽  
pp. 1356-1362 ◽  
Author(s):  
K. S. Kapitan ◽  
P. D. Wagner
Keyword(s):  
Infinite Family ◽  
Inert Gas ◽  
Structural Detail ◽  
The Family ◽  
Single Exception ◽  
Average Distribution ◽  
Log Normal ◽  
Programming Analysis ◽  
Ventilation Perfusion Ratio ◽  
Simple Average

The defining equations of the multiple inert gas elimination technique are underdetermined, and an infinite number of VA/Q ratio distributions exists that fit the same inert gas data. Conventional least-squares analysis with enforced smoothing chooses a single member of this infinite family whose features are assumed to be representative of the family as a whole. To test this assumption, the average of all ventilation-perfusion ratio (VA/Q) distributions that are compatible with given data was calculated using a linear program. The average distribution so obtained was then compared with that recovered using enforced smoothing. Six typical sets of inert gas data were studied. In all sets but one, the distribution recovered with conventional enforced smoothing closely matched the structure of the average distribution. The single exception was associated with the broad log-normal VA/Q distribution, which is rarely observed using the technique. We conclude that the VA/Q distribution conventionally recovered approximates a simple average of all compatible distributions. It therefore displays average features and only that degree of fine structural detail that is typical of the family as a whole.

On the congruence extension property

1997 ◽  
Vol 38 (4) ◽  
pp. 391-394 ◽  
Author(s):  
W.J. Blok ◽  
D. Pigozzi
Keyword(s):  
Extension Property ◽  
Congruence Extension Property
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