Related papers: An Infinite Antichain of Permutations

We generalize Harrington-Marker-Shelah's Dilworth-style characterization of the existence of non-empty perfect antichains to co-analytic quasi-orders, establish the analogous theorem at the next definable cardinal, and consider…

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…

In this paper, we present an algorithm that enumerates a certain class of signed permutations, referred to as grid signed permutation classes. In the case of permutations, the corresponding grid classes are of interest because they are…

A semiring can be ``completed'' (i.e., embedded into a semiring in which all infinite sums are defined and satisfy some reasonable properties) iff this semiring can be naturally partially ordered. This construction is ``natural'' (a left…

We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…

We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for…

The theory of finitely supported algebraic structures represents a reformulation of Zermelo-Fraenkel set theory in which every construction is finitely supported according to the action of a group of permutations of some basic elements…

In this paper we use the Recursion Theorem to show the existence of various infinite sequences and sets. Our main result is that there is an increasing sequence e_0, e_1, e_2 .. such that W_{e_n}={e_{n+1}} for every n. Similarly, we prove…

Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.

This paper is composed of two main results concerning chains of infinite order which are not necessarily continuous. The first one is a decomposition of the transition probability kernel as a countable mixture of unbounded probabilistic…

We consider a stack sorting algorithm where only the appropriate output values are popped from the stack and then any remaining entries in the stack are run through the stack in reverse order. We identify the basis for the $2$-reverse pass…

In this note we show through infinitary derivations that each provably well-founded strict partial order in ${\rm ACA}_{0}$ admits an embedding to an ordinal$<\varepsilon_{0}$.

We consider the partition lattice $\Pi_\kappa$ on any set of transfinite cardinality $\kappa$ and properties of $\Pi_\kappa$ whose analogues do not hold for finite cardinalities. Assuming the Axiom of Choice we prove: (I) the cardinality of…

The simple permutations in two permutation classes --- the 321-avoiding permutations and the skew-merged permutations --- are enumerated using a uniform method. In both cases, these enumerations were known implicitly, by working backwards…

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

In a former paper we introduced partial infinitary noncommutative semigroups and showed, among other, that significant differences arise in comparison with the commutative case, previously studied in the literature. For example, in the…

In classical set theory, the ordinals form a linear chain that we often think of as a very thin portion of the set-theoretic universe. In intuitionistic set theory, however, this is not the case and there can be incomparable ordinals. In…

Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…

Commutative totally ordered monoids abound, number systems for example. When the monoid is not assumed commutative, one may be hard pressed to find an example. One suggested by Professor Orr Shalit are the countable ordinals with addition.…

The periodic (ordinal) patterns of a map are the permutations realized by the relative order of the points in its periodic orbits. We give a combinatorial characterization of the periodic patterns of an arbitrary signed shift, in terms of…