Zobrazeno 1 - 10
of 437
pro vyhledávání: '"Lutz, Patrick"'
Autor:
Cholak, Peter, Csornyei, Marianna, Lutz, Neil, Lutz, Patrick, Mayordomo, Elvira, Stull, D. M.
It is well known that if $A\subseteq\R^n$ is an analytic set of Hausdorff dimension $a$, then $\dim_H(\pi_VA)=\min\{a,k\}$ for a.e. $V\in G(n,k)$, where $\pi_V$ is the orthogonal projection of $A$ onto $V$. In this paper we study how large the except
Externí odkaz:
http://arxiv.org/abs/2411.04959
This paper is devoted to the study of analytic equivalence relations which are Borel graphable, i.e. which can be realized as the connectedness relation of a Borel graph. Our main focus is the question of which analytic equivalence relations are Bore
Externí odkaz:
http://arxiv.org/abs/2409.08624
Autor:
Lutz, Patrick
Conway and Doyle have claimed to be able to divide by three. We attempt to replicate their achievement and fail. In the process, we get tangled up in some shoes and socks and forget how to multiply.
Comment: 6 pages, published in The Mathematica
Comment: 6 pages, published in The Mathematica
Externí odkaz:
http://arxiv.org/abs/2309.11634
Autor:
Lutz, Patrick, Walsh, James
We answer a question of Pakhomov by showing that there is a consistent, c.e. theory $T$ such that no theory which is definitionally equivalent to $T$ has a computable model. A key tool in our proof is the model-theoretic notion of mutual algebraicity
Externí odkaz:
http://arxiv.org/abs/2309.11598
Autor:
Higuchi, Kojiro, Lutz, Patrick
A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this holds for partial orders of height two, but provide evidence that it
Externí odkaz:
http://arxiv.org/abs/2309.01876
Autor:
Lutz, Patrick
We answer a question of Slaman and Steel by showing that a version of Martin's conjecture holds for all regressive functions on the hyperarithmetic degrees. A key step in our proof, which may have applications to other cases of Martin's conjecture, c
Externí odkaz:
http://arxiv.org/abs/2306.05746
Suppose you have an uncomputable set $X$ and you want to find a set $A$, all of whose infinite subsets compute $X$. There are several ways to do this, but all of them seem to produce a set $A$ which is fairly sparse. We show that this is necessary in
Externí odkaz:
http://arxiv.org/abs/2306.01226
Autor:
Lutz, Patrick, Siskind, Benjamin
Martin's Conjecture is a proposed classification of the definable functions on the Turing degrees. It is usually divided into two parts, the first of which classifies functions which are not above the identity and the second of which classifies funct
Externí odkaz:
http://arxiv.org/abs/2305.19646
Autor:
Lutz, Patrick
The Solecki dichotomy in descriptive set theory and the Posner-Robinson theorem in computability theory bear a superficial resemblance to each other and can sometimes be used to prove the same results, but do not have any obvious direct relationship.
Externí odkaz:
http://arxiv.org/abs/2301.07259
Autor:
Lutz, Patrick1 (AUTHOR) pglutz@berkeley.edu
Publikováno v:
Mathematical Intelligencer. Sep2024, Vol. 46 Issue 3, p264-268. 5p.
