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In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for… (More)

We give a criterion involving existence of many generic sequences of automorphisms for a countable structure to have the small index property. We use it to show that (i) any ω-stable ω-categorical structure, and (ii) the random graph has the small index property. We also show that the automorphism group of such a structure is not the union of a countable… (More)

- Robin Hirsch, Ian M. Hodkinson
- J. Symb. Log.
- 1997

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.

- Ian M. Hodkinson, Frank Wolter, Michael Zakharyaschev
- Ann. Pure Appl. Logic
- 2000

In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator (Since or Until) have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for… (More)

- Ian M. Hodkinson
- Ann. Pure Appl. Logic
- 1997

For any finite n ≥ 3 there are two atomic n-dimensional cylindric algebras with the same atom structure, with one representable, the other, not. Hence, the complex algebra of the atom structure of a representable atomic cylindric algebra is not always representable, so that the class RCAn of representable n-dimensional cylindric algebras is not closed under… (More)

In this paper we analyze the decision problem for fragments of first-order extensions of branching time temporal logics such as computational tree logics CTL and CTL or Prior’s Ockhamist logic of historical necessity. On the one hand, we show that the one-variable fragments of logics like first-order C T L —such as the product of propositional C T L with… (More)

We study the complexity of some fragments of firstorder temporal logic over natural numbers time. The onevariable fragment of linear first-order temporal logic even with sole temporal operator2 is EXPSPACE-complete (this solves an open problem of [10]). So are the one-variable, two-variable and monadic monodic fragments with Until and Since. If we add the… (More)

- Johan van Benthem, Nick Bezhanishvili, Ian M. Hodkinson
- Studia Logica
- 2012

We define analogues of modal Sahlqvist formulas for the modal mucalculus, and prove a correspondence theorem for them.

- Ian M. Hodkinson
- Studia Logica
- 2002

We prove decidability of satisfiability of sentences of the monodic packed fragment of firstorder temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. We also prove decidability over models with finite domains, over flows of time including the real order.