#### Filter Results:

#### Publication Year

1994

2016

#### Publication Type

#### Co-author

#### Key Phrase

#### Publication Venue

Learn More

We consider the problem of nding and classifying representations in algebraic logic. This is approached by letting two players build a representation using a game. Homogeneous and universal representations are characterised according to the outcome of certain games. The Lyndon conditions deening representable relation algebras (for the nite case) and a… (More)

Given a representation of a relation algebra we construct relation algebras of pairs and of intervals. If the representation happens to be complete, homogeneous and fully universal then the pair and interval algebras can be constructed direct from the relation algebra. If, further, the original relation algebra is !-categorical we show that the interval… (More)

- Robin Hirsch, Ian Hodkinson, Carl G Jockusch
- 2001

A relation algebra atom structure α is said to be strongly rep-resentable if all atomic relation algebras with that atom structure are rep-resentable. This is equivalent to saying that the complex algebra Cm α is a representable relation algebra. We show that the class of all strongly repre-sentable relation algebra atom structures is not closed under… (More)

A cylindric algebra atom structure is said to be strongly representable if all atomic cylindric algebras with that atom structure are representable. This is equivalent to saying that the full complex algebra of the atom structure is a representable cylindric algebra. We show that for any finite n ≥ 3, the class of all strongly representable n-dimensional… (More)

Two complexity problems in algebraic logic are surveyed: the satisfaction problem and the network satisfaction problem. Various complexity results are collected here and some new ones are derived. Many examples are given. The network satisfaction problem for most cylindric algebras of dimension four or more is shown to be intractable. Complexity is tied-in… (More)

A boolean algebra is shown to be completely representable if and only if it is atomic, whereas it is shown that neither the class of completely representable relation algebras nor the class of completely representable cylindric algebras of any xed dimension are elementary.

We connrm a conjecture about neat embeddings of cylindric algebras made in 1969 by J. D. Monk, connrm a later conjecture by Maddux about relation algebras obtained from cylindric algebras, and solve a problem raised by Tarski and Givant. These results in algebraic logic have the following consequence for predicate logic: for every nite cardinal 3 there is a… (More)

We study relation algebras with n-dimensional relational bases in the sense of Maddux. Fix n with 3 ≤ n ≤ ω. Write B n for the class of non-associative algebras with an n-dimensional relational basis, and RA n for the variety generated by B n. We define a notion of relativised representation for algebras in RA n , and use it to give an explicit (hence… (More)

We characterise the class SRaCA n of subalgebras of relation algebra reducts of n-dimensional cylindric algebras (for finite n ≥ 5) by the notion of a 'hyper-basis', analogous to the cylindric basis of Maddux, and by relativised representations. A corollary is that SRaCA n = SRa(CA n ∩ Crs n) = SRa(CA n ∩ G n). We outline a game-theoretic approximation to… (More)