Some additive properties of special sets of reals
Some Algebraic Properties of Machine Poset of Infinite Words
The complexity of infinite words is considered from the point of view of a transformation with a Mealy machine that is the simplest model of a finite automaton transducer. We are mostly interested in algebraic properties of the underlying partially ordered set. Results considered with the existence of supremum, infimum, antichains, chains and density aspects are investigated.
Some Algebraic Properties of Polynomial Rings
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
Some algebraic properties of weakly compact and compact cardinals
Some applications of game determinacy
Some applications of non-standard analysis to proximity spaces
Some applications of Sargsyan's equiconsistency method
We apply techniques due to Sargsyan to reduce the consistency strength of the assumptions used to establish an indestructibility theorem for supercompactness. We then show how these and additional techniques due to Sargsyan may be employed to establish an equiconsistency for a related indestructibility theorem for strongness.
Some applications of strong Lusin sets
Some automorphisms of natural numbers in the alternative set theory
Some Baire category type theorems for
Some cardinal characteristics of ordered sets
For ordered (= partially ordered) sets we introduce certain cardinal characteristics of them (some of those are known). We show that these characteristics—with one exception—coincide.
Some categories of models.
Some classes of idempotent functions and their compositions
Some combinatorial principles defined in terms of elementary submodels
We give an equivalent, but simpler formulation of the axiom SEP, which was introduced in [9] in order to capture some of the combinatorial behaviour of models of set theory obtained by adding Cohen reals to a model of CH. Our formulation shows that many of the consequences of the weak Freese-Nation property of 𝒫(ω) studied in [6] already follow from SEP. We show that it is consistent that SEP holds while 𝒫(ω) fails to have the (ℵ₁,ℵ ₀)-ideal property introduced in [2]. This answers a question...
Some combinatorial problems, connected with product-isomorphisms of binary relations
Some combinatorial properties of ultrafilters
Some combinatorics involving ultrafilters
Some combinatorics involving ξ-large sets
We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
Some comments on infinite Boolean functions
We introduce infinite Boolean functions and investigate some of their properties.
Some comments on the paper by Artigue, Isambert, Perrin and Zalc