Scott sentences for equivalence structuresSpringer Science and Business Media LLC - Tập 59 - Trang 453-460 - 2019
Sara B. Quinn
For a computable structure $${\mathcal {A}}$$, if there is a computable infinitary Scott sentence, then the complexity of this sentence gives an upper bound for the complexity of the index set $$I({\mathcal {A}})$$. If we can also show that $$I({\mathcal {A}})$$ is m-complete at that level, then there is a correspondence between the complexity of the index set and the complexity of a Scott sentenc...... hiện toàn bộ
SPFA by finite conditionsSpringer Science and Business Media LLC - Tập 55 - Trang 649-661 - 2016
Moti Gitik, Menachem Magidor
Itay Neeman (Norte Dame J Form Log 55:265–298, 2014) presented a new way of iterating of proper forcings. We would like to generalize it here to semi-proper.
Normal subgroups of nonstandard symmetric and alternating groupsSpringer Science and Business Media LLC - Tập 46 - Trang 107-121 - 2007
John Allsup, Richard Kaye
Let
$${\mathfrak{M}}$$
be a nonstandard model of Peano Arithmetic with domain M and let
$${n \in M}$$
be nonstandard. We study the symmetric and alternating groups S
n
and A
...... hiện toàn bộ
Iterated relative recursive enumerabilitySpringer Science and Business Media LLC - Tập 33 - Trang 321-346 - 1994
Peter A. Cholak, Peter G. Hinman
A result of Soare and Stob asserts that for any non-recursive r.e. setC, there exists a r.e.[C] setA such thatA⊕C is not of r.e. degree. A setY is called [of]m-REA (m-REA[C] [degree] iff it is [Turing equivalent to] the result of applyingm-many iterated ‘hops’ to the empty set (toC), where a hop is any function of the formX→X ⊕W
e
X
. The cited ...... hiện toàn bộ
Turing degrees and randomness for continuous measuresSpringer Science and Business Media LLC - - Trang 1-21 - 2023
Mingyang Li, Jan Reimann
We study degree-theoretic properties of reals that are not random with respect to any continuous probability measure (NCR). To this end, we introduce a family of generalized Hausdorff measures based on the iterates of the “dissipation” function of a continuous measure and study the effective nullsets given by the corresponding Solovay tests. We introduce two constructions that preserve non-randomn...... hiện toàn bộ
On Harrop disjunction property in intermediate predicate logicsSpringer Science and Business Media LLC - - Trang 1-8 - 2023
Katsumasa Ishii
A partial solution to Ono’s problem P54 is given. Here Ono’s problem P54 is whether Harrop disjunction property is equivalent to disjunction property or not in intermediate predicate logics. As an application of this result it is shown that some intermediate predicate logics satisfy Harrop disjunction property.