András Pongrácz

The 42 reducts of the random ordered graph

The random ordered graph is the up to isomorphism unique countable homogeneous linearly ordered graph that embeds all finite linearly ordered graphs. We determine the reducts of the random ordered graph up to first-order interdefinability.

A NEW OPERATION ON PARTIALLY ORDERED SETS

Abstract Recently it has been shown that all non-trivial closed permutation groups containing the automorphism group of the random poset are generated by two types of permutations: the first type are permutations turning the order upside down, and the second type are permutations induced by so-called rotations. In this paper we introduce rotations for finite posets, which can be seen as the poset counterpart of Seidel-switch for finite graphs. We analyze some of their combinatorial properties, and investigate in particular the question of when two finite posets are rotation-equivalent. We moreover give an explicit combinatorial construction of a rotation of the random poset whose image is again isomorphic to the random poset. As a corollary of our results on rotations of finite posets, we obtain that the group of rotating permutations of the random poset is the automorphism group of a homogeneous structure in a finite language.

THE UNIVERSAL HOMOGENEOUS BINARY TREE

A partial order is called semilinear iff the upper bounds of each element are linearly ordered and any two elements have a common upper bound. There exists, up to isomorphism, a unique countable existentially closed semilinear order, which we denote by S2. We study the reducts of S2, that is, the relational structures with the same domain as S2 all of whose relations are first-order definable in S2. Our main result is a classification of the model-complete cores of the reducts of S2. From this, we also obtain a classification of reducts up to first-order interdefinability, which is equivalent to a classification of all closed permutation groups that contain the automorphism group of S2.

Reducts of the Henson graphs with a constant

Abstract Let ( H n , E ) denote the Henson graph, the unique countable homogeneous graph whose age consists of all finite K n -free graphs. In this note the reducts of the Henson graphs with a constant are determined up to first-order interdefinability. It is shown that up to first-order interdefinability ( H 3 , E , 0 ) has 13 reducts and ( H n , E , 0 ) has 16 reducts for n ≥ 4 .

Constraint Satisfaction Problems for Reducts of Homogeneous Graphs

For

ON FREE ALGEBRAS IN VARIETIES GENERATED BY ITERATED SEMIDIRECT PRODUCTS OF SEMILATTICES

n\geq 3

Characterizing Translations on Groups by Cosets of Their Subgroups

, let

The complexity of counting quantifiers on equality languages

(H_n, E)

The Complexity of Counting Quantifiers on Equality Languages

denote the

Reconstructing the topology of clones

n