This article is cited in 17 papers

Partial Results in $\Delta_3^0$-Categoricity in Linear Orderings and Boolean Algebras

Ch. F. McCoy

University of Wisconsin-Madison

Abstract: The notion of $\Delta_3^0$-categoricity in linear orderings and Boolean algebras is examined. We provide a proof for the fact that there are uncountably many relatively $\Delta_3^0$-categorical linear orderings, and furnish a proof of another fact which suggests that the (unrelatively) $\Delta_3^0$-categorical linear orderings may be very difficult to classify. In stark contrast to these results for linear orderings, a complete classification of the relatively $\Delta_3^0$-categorical Boolean algebras is given.

Keywords: linear ordering, Boolean algebra, $\Delta_3^0$-categoricity.

UDC: 510.5+510.6

Received: 26.08.2002

 English version: Algebra and Logic, 2002, 41:5, 295–305

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