2 citations · 2 across the 4 of their papers we have counts for
5 papers
Pseudojump inversion in special r. b. classes
Hayden R. Jananthan, Stephen G. Simpson
The Jump Inversion Theorem says that for every real there is a real such that . A known refinement of this theorem says that we…
Very weak fragments of weak Kőnig's lemma
Stephen G. Simpson, Keita Yokoyama
It is well-known that any finite -class of has a computable member. Then, how can we understand this in the context of reverse mathematics? In this note,…
A symmetric -model
Stephen G. Simpson
We prove that there exists a countable -model in which, for all reals and , is definable from if and only is hyperarithmetical in . We also obtain some rel…
Symbolic dynamics: entropy = dimension = complexity
Stephen G. Simpson
Let be the group or the monoid where is a positive integer. Let be a subshift over , i.e., a closed and shift-invariant subset of …
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We exposit two previously unpublished theorems of Leo Harrington.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…