15 papers
Reconstruction of Finite Posets of Width Three
Patrizio Cintioli
We prove that every finite ordered set of width at most three and cardinality at least four is reconstructible from its deck. This settles the width-three part of an open problem p…
Cone Avoidance and the No-Least-Join Theorem
Patrizio Cintioli
We give a column-avoidance modification of the no-least-join construction of Downey, Greenberg, Lewis, and Montalbán. We show that if is computably enumerable, , and…
A Special Class with the Join Property but without Pseudojump Inversion
Patrizio Cintioli
Jananthan and Simpson showed that special classes exist in three of the four possible cases determined by whether the Join Property and the Pseudojump Inversion Property ho…
Pseudo-Hyperjump Inversion Fails for Turing Degrees
Patrizio Cintioli
Jananthan and Simpson asked in Conjecture~4.5 whether every pseudo-hyperjump , with uniformly , admits Turing-degree inversi…
Every introenumerable set contains a uniformly introreducible subset
Patrizio Cintioli
We prove that every infinite introenumerable set contains an infinite uniformly introreducible subset, answering both parts of Question 1.7 of Greenberg, Harrison-Trainor, Patey, a…
A Bounded Finite-One Degree Whose One-One Degrees Form Exactly a Dense Linear Order
Patrizio Cintioli
We construct a set whose bounded finite-one degree, ordered internally by one-one reducibility, consists exactly of a countable dense linear order without endp…
Every Nonrecursive Many-One Degree Contains Either One or Infinitely Many Finite-One Degrees
Patrizio Cintioli
This paper proves that every nonrecursive many-one degree contains either exactly one or infinitely many finite-one degrees. This gives a negative answer to Open Question 2 of Rich…
A Computably Enumerable -Degree Without Computably Enumerable Irreducible -Degrees
Patrizio Cintioli
In this paper, we provide a negative solution to Problem 3 formulated by P.~Odifreddi in his survey articles \textit{``Strong Reducibilities''} (1981) and \textit{``Reducibilities'…
A computably enumerable many-one degree with no least finite-one degree
Patrizio Cintioli
Richter, Stephan, and Zhang asked whether every nonrecursive many-one degree contains a least finite-one degree. We solve this question in the negative, already within the class of…
A strengthened form of Dëgtev's argument and -maximal many-one degrees
Patrizio Cintioli
Dëgtev proved that if a noncomputable computably enumerable set \(U\) satisfies his property \((R)\) and the many-one degree of \(U\) contains no simple set, then the \(1\)-degree…
Dense Chains, Antichains, and Universal Partial Orders Inside a Bounded Finite-One Degree
Patrizio Cintioli
We construct a nonrecursive set \(A\le_T\emptyset'\) and a uniformly computable family of sets \(C_0,C_1,\dots\), all bounded finite-one equivalent to \(A\), such that the correspo…
A -introimmune set in \texorpdfstring{}{Pi01} and introimmunity for several reducibilities
Patrizio Cintioli
We prove that there exists a weak truth-table introimmune set in the class , settling the question left open in previous work of whether the known existence result c…
-Rigidity and Finite-One Degrees Inside Typical Many-One Degrees
Patrizio Cintioli
In recent work, the notion of -rigidity was introduced as a sufficient condition for the existence of infinite antichains of -degrees inside many-one degrees. Motivated by a…
Rigid many-one degrees contain infinite antichains of -degrees
Patrizio Cintioli
Odifreddi asked whether every non-irreducible many-one degree must contain an infinite antichain of one-one degrees. Positive answers are known for computably enumerable many-one d…
On linearly ordered sets of chain components
P. Cintioli, A. Della Corte, M. Farotti
In a dynamical system , with a compact metric space, the chain components, the fundamental building blocks in the Conley decomposition of dynamics, have a natural partia…