ﻻ يوجد ملخص باللغة العربية
We prove that, for any natural number n $ge$ 1, we can find a finite alphabet $Sigma$ and a finitary language L over $Sigma$ accepted by a one-counter automaton, such that the $omega$-power L $infty$ := {w 0 w 1. .. $in$ $Sigma$ $omega$ | $forall$i $in$ $omega$ w i $in$ L} is $Pi$ 0 n-complete. We prove a similar result for the class $Sigma$ 0 n .
We develop general machinery to cast the class of potential canonical Scott sentences of an infinitary sentence $Phi$ as a class of structures in a related language. From this, we show that $Phi$ has a Borel complete expansion if and only if $S_infty
Omega-powers of finitary languages are omega languages in the form V^omega, where V is a finitary language over a finite alphabet X. Since the set of infinite words over X can be equipped with the usual Cantor topology, the question of the topologica
We study the extension of the Kechris-Solecki-Todorcevic dichotomy on analytic graphs to dimensions higher than 2. We prove that the extension is possible in any dimension, finite or infinite. The original proof works in the case of the finite dimens
We study the (parameter) synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero
We study the class of Borel equivalence relations under continuous reducibility. In particular , we characterize when a Borel equivalence relation with countable equivalence classes is $Sigma$ 0 $xi$ (or $Pi$ 0 $xi$). We characterize when all the equ