Absolutely saturated models
Abstract linear dependence.
Abstract Reduction Systems and Idea of Knuth-Bendix Completion Algorithm
Educational content for abstract reduction systems concerning reduction, convertibility, normal forms, divergence and convergence, Church- Rosser property, term rewriting systems, and the idea of the Knuth-Bendix Completion Algorithm. The theory is based on [1].
Abstract -expansions and ultimately periodic representations
For abstract numeration systems built on exponential regular languages (including those coming from substitutions), we show that the set of real numbers having an ultimately periodic representation is if the dominating eigenvalue of the automaton accepting the language is a Pisot number. Moreover, if is neither a Pisot nor a Salem number, then there exist points in which do not have any ultimately periodic representation.
Abzählbarkeit und Wohlordenbarkeit
AC holds iff every compact completely regular topology can be extended to a compact Tychonoff topology
We show that AC is equivalent to the assertion that every compact completely regular topology can be extended to a compact Tychonoff topology.
Accumulation functions on the ordinals
Addendum to “A note on the MacDowell–Specker theorem”
Addendum to "Hyperdefinite stochastic integration III".
Addendum to “On Meager Additive and Null Additive Sets in the Cantor space and in ℝ” (Bull. Polish Acad. Sci. Math. 57 (2009), 91-99)
We prove in ZFC that there is a set and a surjective function H: A → ⟨0,1⟩ such that for every null additive set X ⊆ ⟨0,1), is null additive in . This settles in the affirmative a question of T. Bartoszyński.
Adding a lot of Cohen reals by adding a few. II
We study pairs (V, V₁), V ⊆ V₁, of models of ZFC such that adding κ-many Cohen reals over V₁ adds λ-many Cohen reals over V for some λ > κ.
Adding a random or a Cohen real: topological consequences and the effect on Martin's axiom
Addition and correction to the paper "On stability and products", Fund. Math. 93 (1976), pp. 81-95
Addition of fuzzy quantities: Disjunction-conjunction approach
Addition of initial segments. I.
Addition of initial segments. II.
Addition of rational fuzzy quantities: Convolutive approach
Additive properties and uniformly completely Ramsey sets
We prove some properties of uniformly completely Ramsey null sets (for example, every hereditarily Menger set is uniformly completely Ramsey null).
Adjoint Semilattice and Minimal Brouwerian Extensions of a Hilbert Algebra
Let be a Hilbert algebra. The monoid of all unary operations on generated by operations , which is actually an upper semilattice w.r.t. the pointwise ordering, is called the adjoint semilattice of . This semilattice is isomorphic to the semilattice of finitely generated filters of , it is subtractive (i.e., dually implicative), and its ideal lattice is isomorphic to the filter lattice of . Moreover, the order dual of the adjoint semilattice is a minimal Brouwerian extension of , and the...
Affine spaces as models for regular identities
In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(5) in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and only if the...