5,745 research outputs found
The Fixed Point Property for Posets of Small Width
The fixed point property for finite posets of width 3 and 4 is studied in
terms of forbidden retracts. The ranked forbidden retracts for width 3 and 4
are determined explicitly. The ranked forbidden retracts for the width 3 case
that are linearly indecomposable are examined to see which are minimal
automorphic. Part of a problem of Niederle from 1989 is thus solved
A note on blockers in posets
The blocker of an antichain in a finite poset is the set of
elements minimal with the property of having with each member of a common
predecessor. The following is done:
1. The posets for which for all antichains are characterized.
2. The blocker of a symmetric antichain in the partition lattice is
characterized.
3. Connections with the question of finding minimal size blocking sets for
certain set families are discussed
Fixed-Point Posets in Theories of Truth
We show that any coherent complete partial order is obtainable as the fixed-point poset of the strong Kleene jump of a suitably chosen first-order ground model. This is a strengthening of Visser’s result that any finite ccpo is obtainable in this way. The same is true for the van Fraassen supervaluation jump, but not for the weak Kleene jump
Universal homogeneous causal sets
Causal sets are particular partially ordered sets which have been proposed as
a basic model for discrete space-time in quantum gravity. We show that the
class C of all countable past-finite causal sets contains a unique causal set
(U,<) which is universal (i.e., any member of C can be embedded into (U,<)) and
homogeneous (i.e., (U,<) has maximal degree of symmetry). Moreover, (U,<) can
be constructed both probabilistically and explicitly. In contrast, the larger
class of all countable causal sets does not contain a universal object.Comment: 14 page
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