2,860 research outputs found
Extending Algebraic Operations to D-Completions
In this article we show how separately continuous algebraic operations on T0-spaces and the laws that they satisfy, both identities and inequalities, can be extended to the D-completion, that is, the universal monotone convergence space completion. Indeed we show that the operations can be extended to the lattice of closed sets, but in this case it is only the linear identities that admit extension. Via the Scott topology, the theory is shown to be applicable to dcpo-completions of posets. We also explore connections with the construction of free algebras in the context of monotone convergence spaces. Ā© 2009 Elsevier B.V. All rights reserved
Extending algebraic operations to D -completions
In this article, we show how separately continuous algebraic operations on T0-spaces and the laws that they satisfy, both identities and inequalities, can be extended to theD-completion, that is, the universal monotone convergence space completion. Indeed we show that the operations can be extended to the lattice of closed sets, but in this case it is only the linear identities that admit extension. Via the Scott topology, the theory is shown to be applicable to dcpo-completions of posets. We also explore connections with the construction of free algebras in the context of monotone convergence spaces. Ā© 2011 Elsevier B.V. All rights reserved
Atom structures of cylindric algebras and relation algebras
Accepted versio
Strongly Complete Logics for Coalgebras
Coalgebras for a functor model different types of transition systems in a
uniform way. This paper focuses on a uniform account of finitary logics for
set-based coalgebras. In particular, a general construction of a logic from an
arbitrary set-functor is given and proven to be strongly complete under
additional assumptions. We proceed in three parts. Part I argues that sifted
colimit preserving functors are those functors that preserve universal
algebraic structure. Our main theorem here states that a functor preserves
sifted colimits if and only if it has a finitary presentation by operations and
equations. Moreover, the presentation of the category of algebras for the
functor is obtained compositionally from the presentations of the underlying
category and of the functor. Part II investigates algebras for a functor over
ind-completions and extends the theorem of J{\'o}nsson and Tarski on canonical
extensions of Boolean algebras with operators to this setting. Part III shows,
based on Part I, how to associate a finitary logic to any finite-sets
preserving functor T. Based on Part II we prove the logic to be strongly
complete under a reasonable condition on T
Completed power operations for Morava E-theory
We construct and study an algebraic theory which closely approximates the
theory of power operations for Morava E-theory, extending previous work of
Charles Rezk in a way that takes completions into account. These algebraic
structures are made explicit in the case of K-theory. Methodologically, we
emphasize the utility of flat modules in this context, and prove a general
version of Lazard's flatness criterion for module spectra over associative ring
spectra.Comment: Version 3: Minor corrections. Journal version, up to small cosmetic
change
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