N. A. Bazhenov, R. R. Tukhbatullina, “Computable categoricity of the Boolean algebra <nobr>$\mathfrak B(\omega)$</nobr> with a distinguished automorphism”, Algebra Logika, 2013, Volume 52, Number 2,Pages <nobr>131

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Computable categoricity of the Boolean algebra $\mathfrak B(\omega)$ with a distinguished automorphism

N. A. Bazhenov^a, R. R. Tukhbatullina^b

^a Novosibirsk State University, Novosibirsk, Russia
^b CERGE–EI, a joint workplace of Charles Univ. and Economics Inst. Acad. Sci. Czech Repub., Politických vězňů, 7, 11121 Prague, Czech Republic

Abstract: It is proved that every computably enumerable Turing degree is a degree of categoricity of some computable Boolean algebra with a distinguished automorphism. We construct an example of a computably categorical Boolean algebra with a distinguished automorphism, having a set of atoms in a given computably enumerable Turing degree.

Keywords: Boolean algebra with distinguished automorphism, computable categoricity, categoricity spectrum, degree of categoricity.

UDC: 512.563+510.5+510.6

Received: 24.07.2012