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On regular languages over power sets

Fernando T.

Journal of Language Modelling

2016

Vol. 4, No. 1

29--56

The power set of a finite set is used as the alphabet of a string interpreting a sentence of Monadic Second-Order Logic so that the string can be reduced (in a straightforward way) to the symbols occurring in the sentence. Simple extensions to regular expressions are described matching the succinctness of Monadic Second-Order Logic. A link to Goguen and Burstall’s notion of an institution is forged, and applied to conceptions within natural language semantics of time based on change.

Didactic remarks on the power set

Rygał G., Bryll A.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2011

Vol. 16

331--334

The paper is devoted to correct understanding of the notation for the power set. Often this notation is mistaken with a power of the number 2. The correct definition of the power set is presented as well as several task which an serve for strengthening the understanding of this notion.

Marczewski-Burstin representations of Boolean algebras isomorphic to a power set

Bartoszewicz A.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 3

239-250

The paper contains some sufficient conditions for Marczewski-Burstin representability of an algebra A of sets which is isomorphic to P(X) for some X. We characterize those algebras of sets which are inner MB-representable and isomorphic to a power set. We consider connections between inner MB-representability and hull property of an algebra isomorphic to P(X) and completeness of an associated quotient algebra. An example of an infinite universally MB-representable algebra is given.