8 citations · 26 across the 13 of their papers we have counts for
15 papers
A corrected strategy for proving no finite variable axiomatisation exists for RRA
Rob Egrot, Robin Hirsch
We show that if for all finite there is a pair of non-isomorphic finite digraphs satisfying some additional conditions, one of which is that they cannot be distinguished in a c…
First-order axiomatisations of representable relation algebras need formulas of unbounded quantifier depth
Rob Egrot, Robin Hirsch
Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by…
Seurat games on Stockmeyer graphs
Rob Egrot, Robin Hirsch
We define a family of vertex colouring games played over a pair of graphs or digraphs by players and . These games arise from work on a longstanding open…
Amalgamating poset extensions and generating free lattices
Rob Egrot
We investigate connections between the free lattice generated by a poset while preserving certain bounds and the canonical extension of a poset. Explicitly, we describe how the fre…
Recursive axiomatisations from separation properties
Rob Egrot
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use m…
Order polarities
Rob Egrot
We define an order polarity to be a polarity where and are partially ordered, and we define an extension polarity to be a triple such that $e_X:P\to…
Categories of frame-completions and join-specifications
Rob Egrot
Given a poset , a join-specification for is a set of subsets of whose joins are all defined. The set of downsets closed under join…
Recursive axiomatizations for representable posets
Rob Egrot
We use model theoretic techniques to construct explicit first-order axiomatizations for the classes of posets that can be represented as systems of sets, where the order relation i…
Closure operators, frames, and neatest representations
Rob Egrot
Given a poset and a standard closure operator we give a necessary and sufficient condition for the lattice of -closed sets of to be a frame in t…
No finite axiomatizations for posets embeddable into distributive lattices
Rob Egrot
Let and be cardinals with . We show that the class of posets that can be embedded into a distributive lattice via a map preserving all existing meets and jo…
Non-elementary classes of representable posets
Rob Egrot
A poset is -representable if it can be embedded into a field of sets in such a way that all existing joins, and all existing \emph{finite} meets are preserved. We show that…
Representable posets
Rob Egrot
A poset is representable if it can be embedded in a field of sets in such a way that existing finite meets and joins become intersections and unions respectively (we say finite mee…
Meet-completions and ordered domain algebras
Rob Egrot, Robin Hirsch
Using the well-known equivalence between meet-completions of posets and standard closure operators we show a general method for constructing meet-completions for isotone poset expa…
Preserving meets in meet-dense poset completions
Robert Egrot
Defining P* to be the complete lattice of upsets (ordered by reverse inclusion) of a poset P we give necessary and sufficient conditions on a subset S of P* for P to admit a meet-c…
Completely Representable Lattices
Robert Egrot, Robin Hirsch
It is known that a lattice is representable as a ring of sets iff the lattice is distributive. CRL is the class of bounded distributive lattices (DLs) which have representations pr…