Observation Space And Observables In Classical Mechanics
Observation space and observables in classical mechanics.
On a functional representation of the lattice of projections on a Hilbert space
On a problem of Sikorski in the set representability of Boolean algebras
On a proof of the Erdős-Monk theorem.
On a sufficient condition for strong constructivizability of atomic Boolean algebras.
On a theorem of Baumgartner and Weese
On absolute retracts of ω*
An extremally disconnected space is called an absolute retract in the class of all extremally disconnected spaces if it is a retract of any extremally disconnected compact space in which it can be embedded. The Gleason spaces over dyadic spaces have this property. The main result of this paper says that if a space X of π-weight is an absolute retract in the class of all extremally disconnected compact spaces and X is homogeneous with respect to π-weight (i.e. all non-empty open sets have the same...
On absolutely divergent series
We show that in the -stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P(ω)/fin. This complements Vojtáš’ result that under the two algebras are isomorphic [15].
On automorphism groups of boolean algebras
On automorphisms of Boolean algebras embedded in P (ω)/fin
We prove that, under CH, for each Boolean algebra A of cardinality at most the continuum there is an embedding of A into P(ω)/fin such that each automorphism of A can be extended to an automorphism of P(ω)/fin. We also describe a model of ZFC + MA(σ-linked) in which the continuum is arbitrarily large and the above assertion holds true.
On collections of almost disjoint families
On free Boolean vectors.
On hereditary interval algebras.
On hidden variables
On linear operators strongly preserving invariants of Boolean matrices
Let be the general Boolean algebra and a linear operator on . If for any in (, respectively), is regular (invertible, respectively) if and only if is regular (invertible, respectively), then is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over . Meanwhile, noting that a general Boolean algebra is isomorphic...
On Marczewski-Burstin representable algebras
We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.
On minimal dynamical systems on Boolean algebras
On Monk’s questions
We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.
On semigroups of Boolean ring endomorphisms.