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The PT-order, minimal cutsets and menger property

โœ Scribed by LiBo Yu


Publisher
Springer Netherlands
Year
1989
Tongue
English
Weight
629 KB
Volume
6
Category
Article
ISSN
0167-8094

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๐Ÿ“œ SIMILAR VOLUMES


Maximal chains and cutsets of an ordered
โœ J. -M. Brochet; M. Pouzet ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 797 KB

We prove the following results which are related to Menger's theorem for (infinite) ordered sets. (i) If the space of maximal chains of an ordered set is compact, then the maximum number of pairwise disjoint maximal chains is finite and is equal to the minimum size of a cutset, (i.e. a set which mee

The Menger property for infinite ordered
โœ R. Aharoni; J. -M. Brochet; M. Pouzet ๐Ÿ“‚ Article ๐Ÿ“… 1988 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 549 KB

It is shown that, if an ordered set P contains at most k pairwise disjoint maximal chains, where k is finite, then every finite family of maximal chains in P has a cutset of size at most k. As a corollary of this, we obtain the following Menger-type result that, if in addition, P contains k pairwise

Extensions of ordered sets having the fi
โœ John Ginsburg ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 892 KB

Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being c

The minimal complementation property abo
โœ Andrew E. M. Lewis ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 383 KB

## Abstract Let us say that any (Turing) degree **__d__** > **0** __satisfies the minimal complementation property__ (MCP) if for every degree **0** < **__a__** < **__d__** there exists a minimal degree **__b__** < **__d__** such that **__a__** โˆจ **__b__** = **__d__** (and therefore **__a__** โˆง **_