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It is a classical result of Mortimer that
, first-order logic with two variables, is decidable for satisfiability. We show that going beyond
by adding any one of the following leads to an undecidable logic:– very weak forms of recursion, viz.¶(i) transitive closure...
Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is...
We continue the works of Gurevich-Shelah and Lifsches-Shelah by showing that it is consistent with ZFC that the first-order theory of random graphs is not interpretable in the monadic theory of all chains. It is provable from ZFC that the theory of random graphs is not interpretable in the...
Consider the bounded variable logics
(with k variable symbols), and
(with k variables in the presence of counting quantifiers
). These fragments of infinitary logic
are well known to provide an adequate...
We discuss resource-bounded measures on the class of recursive structures and prove that with respect to such measures a random recursive structure is almost surely isomorphic to the unique countable model of the extension axioms.
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