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Computable structures and operations on the space of continuous functions

Alexander G. Melnikov, Keng Meng Ng (2016)

Fundamenta Mathematicae

We use ideas and machinery of effective algebra to investigate computable structures on the space C[0,1] of continuous functions on the unit interval. We show that (C[0,1],sup) has infinitely many computable structures non-equivalent up to a computable isometry. We also investigate if the usual operations on C[0,1] are necessarily computable in every computable structure on C[0,1]. Among other results, we show that there is a computable structure on C[0,1] which computes + and the scalar multiplication,...

Computing the Rabin Index of a Parity Automaton

Olivier Carton, Ramón Maceiras (2010)

RAIRO - Theoretical Informatics and Applications

The Rabin index of a rational language of infinite words given by a parity automaton with n states is computable in time O(n2c) where c is the cardinality of the alphabet. The number of values used by a parity acceptance condition is always greater than the Rabin index and conversely, the acceptance condition of a parity automaton can always be replaced by an equivalent acceptance condition whose number of used values is exactly the Rabin index. This new acceptance condition can also be...

Concrete quantum logics with generalised compatibility

Josef Tkadlec (1998)

Mathematica Bohemica

We present three results stating when a concrete (=set-representable) quantum logic with covering properties (generalization of compatibility) has to be a Boolean algebra. These results complete and generalize some previous results [3, 5] and answer partiallz a question posed in [2].

Condensation and large cardinals

Sy-David Friedman, Peter Holy (2011)

Fundamenta Mathematicae

We introduce two generalized condensation principles: Local Club Condensation and Stationary Condensation. We show that while Strong Condensation (a generalized condensation principle introduced by Hugh Woodin) is inconsistent with an ω₁-Erdős cardinal, Stationary Condensation and Local Club Condensation (which should be thought of as weakenings of Strong Condensation) are both consistent with ω-superstrong cardinals.

Congruences and ideals in lattice effect algebras as basic algebras

Sylvia Pulmannová, Elena Vinceková (2009)

Kybernetika

Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.

Conjugacy equivalence relation on subgroups

Alessandro Andretta, Riccardo Camerlo, Greg Hjorth (2001)

Fundamenta Mathematicae

If G is a countable group containing a copy of F₂ then the conjugacy equivalence relation on subgroups of G attains the maximal possible complexity.

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