696 research outputs found
Weak Distributivity Implying Distributivity
Let be a complete Boolean algebra. We show, as an application of
a previous result of the author, that if is an infinite cardinal and
is weakly -distributive, then
is -distributive. Using a parallel result, we show
that if is a weakly compact cardinal such that is weakly
-distributive and is -distributive for each , then is -distributive.Comment: 12 page
On regular ultrafilters, Boolean ultrapowers, and Keisler's order
In this paper we analyse and compare two different notions of regularity for
filters on complete Boolean algebras. We also announce two results from a
forthcoming paper in preparation, which provide a characterization of Keisler's
order in terms of Boolean ultrapowers
Natural Factors of the Medvedev Lattice Capturing IPC
Skvortsova showed that there is a factor of the Medvedev lattice which
captures intuitionistic propositional logic (IPC). However, her factor is
unnatural in the sense that it is constructed in an ad hoc manner. We present a
more natural example of such a factor. We also show that for every non-trivial
factor of the Medvedev lattice its theory is contained in Jankov's logic, the
deductive closure of IPC plus the weak law of the excluded middle. This answers
a question by Sorbi and Terwijn
The Isomorphism Relation Between Tree-Automatic Structures
An -tree-automatic structure is a relational structure whose domain
and relations are accepted by Muller or Rabin tree automata. We investigate in
this paper the isomorphism problem for -tree-automatic structures. We
prove first that the isomorphism relation for -tree-automatic boolean
algebras (respectively, partial orders, rings, commutative rings, non
commutative rings, non commutative groups, nilpotent groups of class n >1) is
not determined by the axiomatic system ZFC. Then we prove that the isomorphism
problem for -tree-automatic boolean algebras (respectively, partial
orders, rings, commutative rings, non commutative rings, non commutative
groups, nilpotent groups of class n >1) is neither a -set nor a
-set
Observables in Extended Percolation Models of Causal Set Cosmology
Classical sequential growth models for causal sets provide an important step
towards the formulation of a quantum causal set dynamics. The covariant
observables in a class of these models known as generalised percolation have
been completely characterised in terms of physically well-defined ``stem sets''
and yield an insight into the nature of observables in quantum causal set
cosmology. We discuss a recent extension of generalised percolation and show
that the characterisation of covariant observables in terms of stem sets is
also complete in this extension.Comment: 14 pages, 2 figure
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