After proving this theorem, we obtain similar results for the topological spaces studied in [7] and [11]. Also, cogent examples are given and the relation this note bears to the work of others is discussed. We shall follow the terminology of [5] except we shall assume separation properties for a space only when these assumptions are explicitly stated. For an infinite cardinal m, a set A in a to...

Starting from a model V “ZFC + GCH + κ is supercompact + No cardinal is supercompact up to a measurable cardinal”, we force and construct a model V P such that V P “ZFC + κ is supercompact + No cardinal is supercompact up to a measurable cardinal + δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generaliz...

Abstract Given a cofinal cardinal function $h\in {}^{\kappa }\kappa $ for $\kappa inaccessible, we consider the dominating h -localisation number, that is, least cardinality of set -slaloms such every -real is localised by slalom in set. It was proved [3] localisation numbers can be consistently different two functions (the identity and power function). We will construct ^+$ -sized family their...

The primary visual cortex (V1) of higher mammals contains maps of stimulus features; how these maps influence vision remains unknown. We have examined the functional significance of an asymmetry in the orientation map in cat V1, i.e., the fact that a larger area of V1 is preferentially activated by vertical and horizontal contours than by contours at oblique orientations. Despite the fact that ...

For a cardinal κ and a model M of cardinality κ let No(M) denote the number of non-isomorphic models of cardinality κ which are L∞κ-equivalent to M. In [She82] Shelah established that when κ is a weakly compact cardinal and μ ≤ κ is a nonzero cardinal, there exists a model M of cardinality κ with No(M) = μ. We prove here that if κ is a weakly compact cardinal, the question of the possible value...

When modern set theory is applied to conventional mathematical problems, it has a disconcerting tendency to produce independence results rather than theorems in the usual sense. The resulting preoccupation with “consistency” rather than “truth” may be felt to give the subject an air of unreality. Even elementary questions about the basic arithmetical operations of exponentiation in the context ...

Like people who casually assess similarity between spatial scenes in their routine activities, users of pictorial databases are often interested in retrieving scenes that are similar to a given scene, and ranking them according to degrees of their match. For example, a town architect would like to query a database for the towns that have a landscape similar to the landscape of the site of a pla...

From May 1 to May 6, 2004 24 set theorists met at the Banff International Research Station to discuss Singular Cardinal Combinatorics. Descriptions of the contents of their talks will be published in a Proceedings that will appear in the Notre Dame Journal of Symbolic Logic. During the workshop, several important new results were announced and explained, and there were problem sessions held (so...

Left sided single inferior vena cava is a rare developmental anomaly affecting clinical diagnosis, treatment and raising academic quest. Incidentally, a similar case was found in the museum of the Department of Anatomy of Nepal Medical College. Along with the anomaly, there were other associated vascular anomalies. The article discusses the possible causative situations.

Formation and remodeling of vascular beds are complex processes orchestrated by multiple signaling pathways. Although it is well accepted that vessels of a particular organ display specific features that enable them to fulfill distinct functions, the embryonic origins of tissue-specific vessels and the molecular mechanisms regulating their formation are poorly understood. The subintestinal plex...