S. G. Simpson

activity

20132021

most citedSymbolic dynamics: entropy = dimension = complexity

2 citations · 2 across the 9 of their papers we have counts for

collaborators

10 papers

math.LO2021

Pseudojump inversion in special r. b. $Π_{1}^{0}$ classes

Hayden R. Jananthan, Stephen G. Simpson

The Jump Inversion Theorem says that for every real $A \geq_{T} 0^{'}$ there is a real $B$ such that $A \equiv_{T} B^{'} \equiv_{T} B \oplus 0^{'}$ . A known refinement of this theorem says that we…

math.LO2021

Very weak fragments of weak Kőnig's lemma

Stephen G. Simpson, Keita Yokoyama

It is well-known that any finite $Π_{1}^{0}$ -class of $2^{N}$ has a computable member. Then, how can we understand this in the context of reverse mathematics? In this note,…

math.LO2021

Turing Degrees of Hyperjumps

Hayden R. Jananthan, Stephen G. Simpson

The Posner-Robinson Theorem states that for any reals $Z$ and $A$ such that $Z \oplus 0^{'} \leq_{T} A$ and $0 <_{T} Z$ , there exists $B$ such that $A \equiv_\mathrm{T}…

math.LO2018

A symmetric $β$ -model

Stephen G. Simpson

We prove that there exists a countable $β$ -model in which, for all reals $X$ and $Y$ , $X$ is definable from $Y$ if and only $X$ is hyperarithmetical in $Y$ . We also obtain some rel…

math.LO2017★ 2 cited

Symbolic dynamics: entropy = dimension = complexity

Stephen G. Simpson

Let $G$ be the group $Z^{d}$ or the monoid $N^{d}$ where $d$ is a positive integer. Let $X$ be a subshift over $G$ , i.e., a closed and shift-invariant subset of $A^{G}$ …

math.LO2015

Reverse mathematics, Young diagrams, and the ascending chain condition

Kostas Hatzikiriakou, Stephen G. Simpson

Let $S$ be the group of finitely supported permutations of a countably infinite set. Let $K [S]$ be the group algebra of $S$ over a field $K$ of characteristic $0$ . According to a t…

math.LO2015

Comparing WO $(ω^{ω})$ with $Σ_{2}^{0}$ induction

Stephen G. Simpson

Let WO $(ω^{ω})$ be the statement that the ordinal number $ω^{ω}$ is well ordered. WO $(ω^{ω})$ has occurred several times in the reverse-mathematical literature. The purpose of this expos…

math.LO2014

Mass problems and intuitionistic higher-order logic

Sankha S. Basu, Stephen G. Simpson

In this paper we study a model of intuitionistic higher-order logic which we call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the category of sheaves of s…

math.LO2013

Propagation of partial randomness

Kojiro Higuchi, W. M. Phillip Hudelson, Stephen G. Simpson +1

Let f be a computable function from finite sequences of 0's and 1's to real numbers. We prove that strong f-randomness implies strong f-randomness relative to a PA-degree. We also…

math.LO2013

Harrington's results on arithmetical singletons

Stephen G. Simpson

We exposit two previously unpublished theorems of Leo Harrington. The first theorem says that there exist arithmetical singletons which are arithmetically incomparable. The second…

Pseudojump inversion in special r. b. Π10​ classes

Very weak fragments of weak Kőnig's lemma

Turing Degrees of Hyperjumps

A symmetric β-model

Symbolic dynamics: entropy = dimension = complexity

Reverse mathematics, Young diagrams, and the ascending chain condition

Comparing WO(ωω) with Σ20​ induction

Mass problems and intuitionistic higher-order logic

Propagation of partial randomness

Harrington's results on arithmetical singletons

Pseudojump inversion in special r. b. $Π_{1}^{0}$ classes

A symmetric $β$ -model

Comparing WO $(ω^{ω})$ with $Σ_{2}^{0}$ induction